SCERT AP 7th Class Maths Solutions Pdf Chapter 10 Construction of Triangles Review Exercise Questions and Answers.

## AP State Syllabus 7th Class Maths Solutions 10th Lesson Construction of Triangles Review Exercise

Question 1.

Draw the angles 70° and 110° by using a protractor,

(i) ∠AOB = 70°

Answer:

∠AOB = 70°

- Draw a ray \(\overrightarrow{\mathrm{OA}}\)
- At ‘O’ erect a ray OB such that ∠AOB = 70°

(ii) ∠AOB = 110°

Answer:

∠AOB = 110°

- Draw a ray \(\overrightarrow{\mathrm{OA}}\).
- At ‘O’ erect a ray \(\overrightarrow{\mathrm{OB}}\) such that ∠AOB = 110°

Question 2.

Construct the angles 60° and 120° by using ruler and compass.

(i) ∠AOB = 60°

Answer:

∠AOB = 60°

- Draw a ray \(\overrightarrow{\mathrm{OA}}\).
- Draw an arc with any radius (convenient) taking ‘O’ as a centre and cutting \(\overrightarrow{\mathrm{OA}}\) at X.
- Draw an arc with the same radius – taking X as a centre and meeting the previous arc at Y.
- Join OY and produce it to B.
- ∠AOB is formed.
- ∠AOB = 60°

(ii) ∠ADI = 120°

Answer:

∠ADI = 120°

- Draw a ray \(\overrightarrow{\mathrm{DA}}\).
- Draw an arc with any radius taking ‘D’ as centre intersecting \(\overrightarrow{\mathrm{DA}}\) at X.
- Now draw two successive arcs from X intersecting the previous arc at Y and Z.
- Join D and Z and produce DZ to I.
- Now the angle formed ∠ADI is equal to 120°.

Question 3.

Draw a line segment PQ = 4.5 cm and construct its perpendicular bisector by using ruler and compass.

Answer:

∠PMY = ∠QMY = 90°

So, PQ ⊥ XY

- Draw a line segment PQ of length 4.5 cm.
- Draw two arcs with centre P and radius > \(\frac{1}{2}\)PQ on both sides of PQ.
- Repeat step 2 with centre ‘Q’ intersecting the previous arc at X and Y.
- Join X and Y and produce it on either sides to form \(\overrightarrow{\mathrm{XY}}\).
- XY is the perpendicular bisector of PQ.

Question 4.

Construct ∠DEF = 60° and its angular bisector by using ruler and compass.

Answer:

∠DEF = 60°

∠DEK = ∠FEK = \(\frac{\angle \mathrm{DEF}}{2}=\frac{60^{\circ}}{2}\) = 30°

- Construct ∠DEF = 60°
- Draw an arc with a convenient radius taking E as centre intersecting ED at X and EF at Y.
- Draw two arcs with the same radius taking X and Y as centres intersecting at Z.
- Join E, Z and produce it to K.
- ∠DEK = ∠KEF = 30°.

Question 5.

Construct an angle of 90° without using a protractor.

Answer:

∠SRI = 90°

- Draw a ray \(\overrightarrow{R S}\).
- Draw an arc of convenient radius taking R as a centre and intersecting \(\overrightarrow{R S}\) at X.
- With the same radius draw two successive arcs from X intersecting the previous arc at Y & Z.
- Draw bisector to \(\widehat{\mathrm{YZ}}\) intersecting at I.
- Join R, I.