Srinivas AP State Syllabus AP Board 7th Class Maths Solutions Chapter 15 Symmetry Ex 4 Textbook Questions and Answers.
Question 1.
Some english alphabets have fascinating symmetrical structures. Which capital letters have only one line of symmetry (like E))’? Which capital letters have rotational symmetry of order 2 (like I)’?
Fill the following table, thinking along such lines.
Solution:
AP State Syllabus AP Board 7th Class Maths Solutions Chapter 15 Symmetry Ex 3 Textbook Questions and Answers.
Question 1.
Which of the following figures have rotational symmetry of order more than 1?
Solution:
The above figure (i), (ii), (iii), (iv), (v) have rational symmetry of order more than 1.
Question 2.
Give the order of rotational symmetry for each figure.
Solution:
(i) Order 2
(ii) Order 4
(iii) Order 3
(iv) Order 4
(v) Order 4
(vi) Order 5
(vii) Order 6
(viii) Order 3
AP State Syllabus AP Board 7th Class Maths Solutions Chapter 15 Symmetry Ex 2 Textbook Questions and Answers.
Question 1.
In the figures given below fmd the axes of symmetry such that on folding along the axis the two dots fall on each other.
Solution:
Question 2.
Given the line of symmetry, find the other dot.
Solution:
Question 3.
In the following incomplete figures, the mirror line (i.e. the line of symmetry) is given as a dotted line. Complete each figure, pcrlorming reflection on the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Are you able to recall the name of the figure you complete’?
Solution:
Question 4.
State whether the following statements are true or false.
(i) Every closed figure has an axis of symmetry. ( )
(ii) A figure with at least one axis of symmetry is called a symmetric figure. ( )
(in) A regular polygon of 10 sides will have 12 axes of symmetry. ( )
Solution:
(i) False
(ii) True
(iii) False
Question 5.
Draw a square and construct all its axes of symmetry. Measure the angles between each pair of successive axes of symmetry. What do you notice? Does the same rule apply for other regular polygons’?
Solution:
Angle between successive axes of
Symmetry = 45° = \(\frac{360^{\circ}}{2 \mathrm{n}}\)
This is true for all regular polygons.
AP State Syllabus AP Board 7th Class Maths Solutions Chapter 15 Symmetry Ex 1 Textbook Questions and Answers.
Question 1.
Given below are some fiugres. Which of them are symmetric? Draw the axes of symmetry
for the symmetric figures.
Solution:
Students can go through AP State Board 9th Class Biology Notes Chapter 9 Adaptations in Different Ecosystems to understand and remember the concept easily.
→ Adaptation is a physiological or structural characteristic of an organism, becomes suited to a particular environment
→ Organisms in nature create adaptable situations around them on the basis of their needs.
→ Organisms need shelter, food, light, air and many other things for their survival
→ Adaptations in xerophytic plants are succulent stems, reduced leaves and have a deep root system.
→ Animals living in the deserts also show adaptive characteristic features.
→ Microscopic planktons have droplets of oil in their cells that keeps them float
→ Each form of marine life has become adapted to a specific area with a relatively narrow variation in salinity, temperature and light
→ Aquatic animals have certain adaptations to fight the pressure of the underwater current
→ Marine life has adapted to an incredible variety of conditions and habitats.
→ Marine adaptations include symbiosis, camouflage, defensive behaviour, reproductive strategies etc.
→ The marine ecosystem is divided into euphotic zone, bathyal zone and abyssal zone.
→ Based on the light penetration freshwater ecosystem is divided into a littoral zone, limnetic zone and profundal zone.
→ Partially submerged plants have numerous air spaces inside the stems, leaves, roots that aid in gaseous exchange and buoyancy.
→ Plants in temperate regions shed their leaves before the winter.
→ In tropical regions, some plants shed their leaves before the start of summer.
→ Animals living in cold regions have a thick layer of fat or thick fur coat covering their bodies.
→ To protect themselves from the extremes of hot and cold conditions, animals adapt to hibernation and aestivation. E.g.: frog
→ Animals living in the bottom layers of the sea are scavengers or predators are one usually blind
→ Mangroves: Plants grown at seashores. Growing ¡na wet and salty places.
→ Precise: Exact, accurate.
→ Adaptations: It ¡s a feature that ¡s common in any population because it provides some improvements for better survival.
→ Succulent stem: Water is stored in the tissues of the stem.
→ Xerophytes: Plants that were grown in fewer water areas like deserts.
→ Scorching: Burn superficially.
→ Pebble plants: Smooth, round water-storing plants leave store water.
→ Ornamental plants: Decorative plants are kept in pots at homes.
→ Adder snake: A small poisonous snake often with diamond-shaped marks on its back.
→ Nocturnal: Animals that are active during the night.
→ Beneath: Lower position.
→ Strenuous: Energetic
→ Ecosystem: Unit of a biosphere. It comprises both biotic and abiotic components.
→ Incredible: Impossible or very difficult to believe.
→ Blubber: The fat of whales and other sea animals.
→ Photosynthesis: It ¡s the process of preparing carbohydrates by plants in the presence of sunlight, chlorophyll, water and carbon dioxide. It is an anabolic process.
→ Respiration: It ¡s a catabolic process. Carbohydrates are broken down into water and carbon dioxide releasing energy.
→ Barnacles: Fish that attaches itself to objects underwater. e.g. Ample to rocks and bottoms of ships.
→ Transpiration: The loss of water vapour from a plant, especially through the stomata.
→ Herring gulls: A large North Atlantic bird of gull family with black tips to its wings.
→ Camouflage: The way in which an animal’s colours or shape matches its surroundings and makes ¡t difficult to see.
→ Symposium: A small conference. A meeting at which experts have discussions about a particular subject.
→ Trout: A common freshwater fish that is used for food.
→ Herring: A North Atlantic fish that swims ¡n very large groups and is used for food.
→ Bioluminescence: Refers to the production of light by living organisms. It ¡s common in deep-sea organisms, and in some insects. e.g. Fireflies.
→ Puddle: Small amount of water or liquid especially rain that has collected in one place on the ground.
→ Scavengers: Animal feeding on dead organisms which it has not killed.
→ Euphotic zone: The top layer of a sea through which light can penetrate, allowing photosynthesis to take place. It is usually 200 m in depth.
→ Bathyal zone: It is usually 200 m to 2000 m depth. Dimly light can penetrate. Light is not sufficient to perform photosynthesis.
→ Abyssal zone: The zone from 2000 m to 6000 m depth. There is no light and always dark.
→ Littoral zone: The shallow zone near the seashore. The water near the shore is usually muddy.
→ Limnetic zone: It is the open water zone at the top of the water body that receives a good deal of light.
→ Profundal zone: It ¡s dimly light and cold. Most heterotrophs are found in this region.
→ Phytoplanktons: Free-floating plants living near the surface oía sea or lake.
→ Amphibians: Animals that can live in water and also on land. E.g.: Frogs, toads etc.
→ Aestivation: Summer sleep. This refers to a state of inactivity which some animals undergo during long periods of drought or heat.
→ Hibernation: Winter sleep.
→ Crustacean: Any creature with a soft body that ¡s divided into sections and a hard out shell. E.g.: Crabs, shrimps etc.
→ Wading birds: Birds walk or move with difficulty ¡n water.
→ Finch: A small bird with a sharp beak. Our state bird is also a finch.
→ Though these are called Living stones they are not stones. The swollen leaves are adapted to desert conditions, minimizing water loss and storing water. These are also called Pebble Plants. Each pebble is actually a leaf with a cut window that lets in light. The stone-like appearance deceives the animals and saves them from being eaten.
→ Animals that are active during the night and sleep during the day are called Nocturnals. These creatures generally have highly developed senses of hearing and smell. They have especially adapted eyesight to see well in dark. Animals like bats, emit a high pitched sound that bounces off objects to find prey or protect from predators.
Cats, Rats, Bats, Owls are the Nocturnals generally seen in our surroundings. Some insects like crickets, firefly and fishes like cuttlefish are active during the night only. Some desert animals become nocturnals in order to escape extreme daytime heat.
→ Electric Eel is an electric fish. It is capable of generating powerful electric shocks of up to 600 Volts when uses for hunting self-defence. It is an apex predator. Despite its name, it is not an eel, but rather a knife fish.
→ Charles Darwin (1809 – 1882):
AP State Syllabus AP Board 7th Class Maths Solutions Chapter 14 Understanding 3D and 2D Shapes Ex 4 Textbook Questions and Answers.
Question 1.
A bulb is kept burning just right above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You may try to experiment first and then answer these questions).
Solution:
A ball -Circle
A cylindrical pipe – Rectangle
A book – Rectangle
Question 2.
Here are the shadows of some 3D objects, when seen under the lamp of an overhead projector. Identify the solid(s) that match each shadow. (There may be many answers for these!)
Solution:
i) A Circle – Spherical/circular objects
ii) A Square – Cube/square sheets
iii) A Triangle – Triangular/right prism with triangular base
iv) A Rectangle – Cuboid/rectangular shapes.
AP State Syllabus AP Board 7th Class Maths Solutions Chapter 14 Understanding 3D and 2D Shapes Ex 3 Textbook Questions and Answers.
Question 1.
Use an isometric dot paper and make an isometric sketch for each one of the given shapes.
Solution:
Question 2.
The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.
Solution:
Question 3.
Three cubes each with 2 cm edge are placed side by side to form a cuboid. Draw an oblique or isometric sketch of this cuboid.
Solution:
Question 4.
Make an oblique sketch for each of the given isometric shapes.
Solution:
Question 5.
Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:
(a) A cuboid of dimensions 5 cm, 3 cm and 2 cm. (Is your sketch unique’?)
(b) A cube with an edge 4 cm long.
Solution:
AP State Syllabus AP Board 7th Class Maths Solutions Chapter 14 Understanding 3D and 2D Shapes Ex 2 Textbook Questions and Answers.
Question 1.
Some nets are given below. Trace them and paste them on a thick paper. Try to make 3-D
shapes by suitably folding them and gluing together. Match the net with it’s 3-D shape.
Nets
3D shapes
(i)
Solution:
Question 2.
Three nets for each shape are given here. Match the net with its 3-D shape.
Solution:
Solution:
Solution:
Question 3.
A dice is a cube with dots on each face. The opposite faces of a dice always have a total of seven dots on them.
Here are two nets to make dice. Insert the suitable number of dots in blanks.
Solution:
AP State Syllabus AP Board 7th Class Maths Solutions Chapter 14 Understanding 3D and 2D Shapes Ex 1 Textbook Questions and Answers.
Question 1.
Given below are the pictures of some objects. Categorise and fill write their names according to their shape and fill the table with name of it.
Solution:
Question 2.
Write names of at least 2 objects from day-to-day life, which are in the shape of the basic 3D shapes given below:
(i) Cone – ……………
(ii) Cube – ……………
(iii) Cuboid – ……………
(iv) Sphere – ……………
(v) Cylinder – ……………
Solution:
i) Cone : Ice-cream cone, birthday caps
ii) Cube : Die, chalk piece box
iii) Cuboid : Eraser, brick
iv) Sphere : Marbles, balls
v) Cylinder: Pencil, candle, pipe
Question 3.
Identify and state the number of faces, edges and vertices of the figures given below:
Solution:
AP State Syllabus AP Board 7th Class Maths Solutions Chapter 9 Construction of Triangles InText Questions and Answers.
Try This
Question 1.
Construct a triangle with the same measurements given in above example taking PQ as base. Are the triangles congruent ? (Page No. 183)
Solution:
PQ = 4 cm, QR = 5 cm. RP = 7cm.
Step -1 : Draw a rough sketch of the triangle and label it with the given measurements.
Step – 2 : Draw a line segment PQ of length 4 cm.
Step – 3 : With centre P, drawn an arc of radius 7 cm.
Step – 4 : Since R is at a distance of
5 cm from Q. draw another arc from Q with radius 5 cm such that it intersects first arc at R.
Step – 5 : Join P, R and Q, R. The required APQR is constructed.
The two triangles are congruent by Side – Side – Side (SSS) criterion for congruence.
Question 2.
Construct a ΔPET, PE = 4.5 cm, ET = 5.4 cm and TP = 6.5 cm in your notebook. Now construct ΔABC, AB = 5.4 cm, BC = 4.5 cm and CA = 6.5 cm on a piece of paper. Cut it out and place it on the figure you have constructed in your notebook. Are the triangles congruent ? Write your answer using mathematical notation. (Page No. 183)
Solution:
ΔPET, PE = 4.5 cm, ET = 5.4 cm, TP = 6.5 cm.
Step – 1 : Draw a rough sketch of the triangle and label it with the given measurements.
Step – 2 : Draw a line segment PE of length 4.5 cm.
Step – 3 : With centre P, draw an arc of radius 6.5 cm.
Step – 4 : Draw another arc from E with radius – 5. 4 cm such that it intersets first arc at T.
Step – 5 : Join P, T and E, T. The required APET is constructed.
ΔABC, AB = 5.4 cm, BC = 4.5 cm and CA = 6.5
Step – 1 : Draw a rough sketch of the
triangle and label it with the given measurements.
Step – 2 : Draw a line segment AB of length 5.4 cm.
Step – 3 : With centre A, draw an arc of radius 6.5 cm.
Step – 4 : Draw another arc from B
with radius 4.5 cm such that it intersects first arc at C.
Step – 5 : Join A, C and B,C. The required AABC is constructed.
If we place the ΔABC on ΔPET, the triangles are congruent. This is because,
AB = TE
AC = PT
BC = PE
∴ ΔABC ≅ ΔTEP (SSS criteria)
Question 3.
Sushanth prepared a problem. Construct ΔXYZ in which XY = 2 cm, YZ = 8 cm and XZ = 4 cm. He also draw the , rough sketch as shown in figure (i).
Reading the problem, Srija told Sushanth that it would not be possible to draw a triangle with the given measurements. However, Sushanth started to draw the diagram as shown in figure (ii).Check whether Sushanth can draw the triangle. If not, why ?
Discuss with your firends. What property of triangles supports Srija’s idea ? (Page No. 184)
Solutuion:
XY = 2 cm, YZ = 8 cm, XZ = 4 cm
Sushanth can not draw the triangle. This is because, in a triangle, the sum of any two sides of a triangle is greater than its third side. But in this case, sum of the two sides is not greater than the third side.
That is XY + XZ ≯ YZ
2 + 4 ≯ YZ
So, it is not possible to construct a triangle with the given measurements.
Question 4.
Construct a triangle with angles 105° and 95° and a side of length of your choice. Could you construct the triangle ? Discuss and justify. (Page No. 187)
Solution:
Let PQ = 5 cm, ∠P = 105°, ∠Q = 95°
We cannot construct a triangle with these measurements. This is because, the sum of three angles in a triangle is 180°. But the sum of the given two angles itself is greater than 180°.
That is 105° + 95° = 200° > 180°
So, it is not possible to construct a triangle with angles 105° and 95°.
AP State Syllabus AP Board 7th Class Maths Solutions Chapter 13 Area and Perimeter Ex 6 Textbook Questions and Answers.
Question 1.
A path 2.5 m wide is running around a square field whose side is 45 m. Determine the area of the path.
Solution:
Area of the path= (Area of outer figure) – (Area of inner figure)
= (50 × 50) – (45 × 45)
= 2500 – 2025 = 475 m2
Question 2.
The central hail ofa school is 18m long and 12.5 m wide. A carpet is to be laid on the floor leaving a strip 50 cm wide near the walls, uncovered. Find the area of the carpet and also the uncovered portion?
Solution:
Given
Length of the hail = 18m
Breadth of the hail 12.5m
Width of the strip = 50cm = \(\frac { 1 }{ 2 }\)m
Length of inner rectangle = 18 – (\(\frac { 1 }{ 2 }\) + \(\frac { 1 }{ 2 }\)) 17m
Breadth of inner rectangle = 12.5 – (\(\frac { 1 }{ 2 }\) + \(\frac { 1 }{ 2 }\)) = 11.5 m
Area of the strip = (Area of the outer fIgure) – (Area of the inner figure)
= 18 × 12.5 – 17 ×11.5
= 225 – 195.5 = 29.5 m2
∴ Area of the carpet = 195.5 m2
Question 3.
The length of the side of a grassy square plot is 80 m. Two walking paths each 4m wide
are constructed parallel to the sides of the plot such that they cut each other at the centre
of the plot. Determine the area of the paths.
Solution:
Given : A square grassary plot of length 80m
Two paths of width 4m each.
From the question
KL = 4m and KN = 80m
EH = 4m and EF 80m
PQ = 4m and PS 4m
Area of two paths = 🖾 KLMN + 🖾 EFGH – 🖾 FQRS
= KN x KL + EF × EH – PQ × PS
= 80 × 4 + 80 × 4 – 4 × 4
= 320 + 320 – 16
= 624sq.m.
Question 4.
A verandah 2 m wide is constructed all around a room of dimensions 8 m X 5 m. Find the area of the verandah
Solution:
Length of outer rectangle = 8 + 2 + 2 =12m
Breadth of outer rectangle = 5 + 2 + 2 = 9m
Area of outer rectangle = l x b = 12 × 9 = 108m2
Length of inner rectangle = 8m
Breadth of inner rectangle = 5m
Area of inner rectangle = l x b = 8 × 5 = 40m2
:. Area of the verandah = (Area of outer figure) – (Area of inner figure)
= 108 – 40 = 68m2
Question 5.
The length of a rectangular park is 700 m and its breadth is 300 m. Two crossroads, each of width 10 m, cut the centre of a rectangular park and are parallel to its sides. Find the area of the roads. Also, find the area of the park excluding the area of the crossroads.
Solution:
Given
Length of the rectangular park = 700 m
Breadth of the rectangular park = 300 ni
From the question,
PS 10m. PQ = 700 ni
Area of 🖾 PQRS = 10 × 700 = 7000m2
AB = 10m, AD = 300m
Area of 🖾 ABCD = 300 x 10 3000m2
KL = 10m, KN = 10m
🖾 KLMN = 10 × 10 = 100m2
Area of the two paths = 🖾 IQRS + 🖾 AF3CD – 🖾 KLMN
= 7000 + 3000 – 100
= 9900m2
The remaining area of the park = Area of the whole park – Area of the two paths
= 700 × 300 – 9900
= 210000 – 9900
= 200100 q.m.
Andhra Pradesh AP Board 3rd Class Maths Solutions 9th Lesson Shapes Around Us Textbook Exercise Questions and Answers.
Textbook Page No. 104
1. Tick (✓) the correct view of the different items (Top/Front/Side).
a)
Answer:
b)
Answer:
c)
Answer:
d)
Answer:
Question 2.
Look at the pictures and write the view of the picture (Top/Side/Front)
Answer:
Textbook Page No. 105
Answer:
Answer:
Activity :
a) Draw Side, Top and Front view pictures of an eraser.
Answer:
b) Match the object with the shapes. One is done for you.
Answer:
Textbook Page No. 106
Rolls and Slides :
I. Which one slides and which one rolls?
Which one slides and which
A) ____ slides
Answer:
book
B) _____________rolls
Answer:
ball
Activity :
Observe the above pictures and list the objects that:
Answer:
Textbook Page No. 107
Observe the objects in the above picture and classify
Answer:
Do these:
a) Observe the following pictures. Mark ‘C’ against curved surface objects. Mark ‘F’ against the flat surface objects.
Answer:
Textbook Page No. 108
II.
Look at the picture and answer the following questions:
Question 1.
Who are standing at corners ?
Answer:
Dheeraj, Sarala, Rafi and Vani are at corners.
Question 2.
Who is out ?
Answer:
David is out
Question 3.
Who are not out ?
Answer:
Bindu andDheeraj, Sarala, Rafi and Vani.
Question 4.
Why they are not out ?
Answer:
They are at corners and middle of the cot.
Textbook Page No. 109
Do these :
a) Colour the faces of these objects with orange, edges with blue and corners with red.
Answer:
III. Stamping:
Take an eraser. Press it on ink pad. Stamp its impression in the space provided. Repeat the same with the objects given in the table.
Stamp images of the given objects :
The image is called face of the object
Textbook Page No. 110
Activity
Take an eraser / small toothpaste box trace three different faces along all its edges.
IV Observe the given real life objects and fill the table according to their shape.
Answer:
Fill the table matching the shapes with their names.
Answer:
Textbook Page No. 111
V. Count the number of 
shapes in the picture given below and colour them as per your choice.
Observe the
a) number of 
s = _____________
Answer: 41
b) number of 
s = ____
Answer: 26
c) number of 
s = ____
Answer: 10
d) number of 
s = ____
Answer: 17
VI. Maths Lab Activity: (Observe the shadow of the objects)
Take book, ball, pencil box, plate, joker cap, glass, duster, chess board etc., Focus a torch on each object so that the image forms on the wall’ as shown in the figures. Change the object each time and observe the shade on the wall. Draw the shape of the image in the table given below.
Textbook Page No. 112
Answer:
Textbook Page No. 113
Activity – 1
Children ! Take a mirror. Keep it on the line. Observe the full picture. Then remove the mirror and draw the other half. One is done for you.
Answer:
Textbook Page No. 114
Activity – 2
Look at the pictures given below. Divide them into equal halves with a dotted line. One is done for you. Draw such lines as many as possible to each picture.
Answer:
Do these
I. Look at the pictures given below. Do the dotted lines divide the pictures into two equal halves? If so, mark them with a (✓) mark.
Answer:
II. Match the following pictures with their other halves.
Answer:
III. Draw the other half of these pictures. Check with a mirror.
Answer:
Textbook Page No. 115
Exercise 1
1. Write the view of the following.
a)
Answer:
Top
b)
Answer:
Front
c)
Answer:
Side
2. Write which one slides (or) rolls.
a)
Answer:
Rolls
b)
Answer:
Slides
c)
Answer:
Rolls
3. Draw the other of the following pictures.
a)
Answer:
b)
Answer:
4. Extend the following patterns.
a)
Answer:
b)
Answer:
Textbook Page No. 116
Observe the pattern and draw the shape that should come next. One is done for you.
Example:
1.
Answer:
2.
Answer:
3.
Answer:
4.
Answer:
5.
Answer:
6.
Answer:
7.
Answer:
8.
Answer:
Multiple Choice Questions
Question 1.
Among the following which object rolls ? ( )
A) Duster
B) Dice
C) Geomtery box
D) Tomato
Answer:
D) Tomato
Question 2.
Among the following which object slides ? ( )
A) Tomoto
B) Wheel
C) Ring
D) Book
Answer:
D) Book
Question 3.
Choose half of the picture given. ()
Answer:
Question 4.
Complete the pattern.
Answer:
II. Take book, ball, pencil box, plate, joker cap, glas, duster, chess board etc., Focus a torch on each object so that the image forms on the wall as shown in the figure.
5. The shape of the shadow of ball is ……….
Answer:
(circle)
6. The shape of the shadow of joker cap is
Answer:
(Triangle)
7. The shape at the shadow of Pencil is ………….
Answer:
(line)
8. Among the following which letters were not possible to divide equally.
Answer:
G, J, Q, C
9. Complete the pattern.
Answer:
