Practice Set 3.5 Geometry 9th Std Maths Part 2 Answers Chapter 3 Triangles
Question 1
Maharashtra Board Solution
If ∆XYZ ~ ∆LMN, write the corresponding angles of the two triangles and also write the ratios of corresponding sides.
Solution & Step-by-Step Answer:
∆XYZ ~ ∆LMN [Given] ∴ ∠X ≅ ∠L ∠Y ≅ ∠M > ∠Z ≅ ∠N [Corresponding angles of similar triangles] [Corresponding sides of similar triangles]
Question 2
Maharashtra Board Solution
In ∆XYZ, XY = 4 cm, YZ = 6 cm, XZ = 5 cm. If ∆XYZ ~ ∆PQR and PQ = 8 cm, then find the lengths of remaining sides of ∆PQR.
Solution & Step-by-Step Answer:
∆XYZ ~ ∆PQR [Given] ∴ [Corresponding sides of similar triangles] ∴ PR = 10 cm ∴ QR = 12 cm, PR = 10cm
Question 3
Maharashtra Board Solution
Draw a sketch of a pair of similar triangles. Label them. Show their corresponding angles by the same signs. Show the lengths of corresponding sides by numbers in proportion.
Solution & Step-by-Step Answer:
∆GHI ~ ∆STU
Maharashtra Board Class 9 Maths Chapter 3 Triangles Practice Set 3.5 Intext Questions and Activities
Question 1
Maharashtra Board Solution
We have learnt that if two triangles are equiangular then their sides are in proportion. What do you think if two quadrilaterals are equiangular? Are their sides in proportion? Draw different figures and verify. Verify the same for other polygons. (Textbook pg no 50)
Solution & Step-by-Step Answer:
If two quadrilaterals are equiangular then their sides will not necessarily be in proportion. Case 1: The two quadrilaterals are of the same type. Consider squares ABCD and PQRS. ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R, ∠D = ∠S
Case 2: The two quadrilaterals are of different types.
Consider square ABCD and rectangle STUV.
∠A = ∠S, ∠B = ∠T, ∠C = ∠U, ∠D = ∠V