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6. Similarity of Triangles
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Q8 of 70 Page 120

For ΔABC and ΔXYZ, ABC ↔ XYZ is a similarity. If , AC = 3 and XY = 5, find YZ and XZ.

Given, For ΔABC and ΔXYZ, ABC ↔ XYZ is a similarity


And AC = 3 and XY = 5


Hence,


AB = 4 and BC = 6


Due to similarity of both the triangles,




⟹ YZ = = 7.5


And,


⟹ XZ = = 3.75


More from this chapter

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6

In ΔXYZ ~ ΔDEF consider the correspondence XYZ ↔ EDF.

If find and .

7

Using the definition of similarity prove that all the isosceles right angled triangles are similar.

9

State whether the following statements are true or false. Give reasons for your answer:

(1) If ΔPQR and ΔABC are similar and none of them is equilateral, then all the six correspondences between ΔPQR and ΔABC are similarities.


(2) All congruent triangles are similar.


(3) All similar triangles are congruent.


(4) If the correspondences ABC ↔ BAC is similarity, then AABC is an isosceles triangle.


(5) The correspondence PQR ↔ YZX between ΔPQR and ΔYZX is a similarity. If m∠P = 60, m∠R = 40, then m∠Z = 80.

10

ΔABC ~ ΔPQR for the correspondence ABC ↔ QRP. If m∠A = 50, m∠C = 30, then m∠R =

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6. Similarity of Triangles
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