Page 197 - Start Up Mathematics_7

7. State the correspondence between the parts if
(a) ∆ PQR ≅ ∆ XYZ (b) ∆ OPT ≅ ∆ FUG

D C
8. In the adjoining figure, DC || AB, AD = BC. Prove using
the concept of congruent triangles that AE = BF.

A E F B

9. Draw a diagram for the following statements and prove the result.
(a) In an isosceles triangle, the median joining the vertex (formed by intersection of equal
sides) to the midpoint of opposite side is also an altitude.
(b) Any two altitudes of an equilateral triangle are congruent.

D C

10. In the adjoining figure, DA = CB and AX = BY. Prove
that ∆ DAY ≅ ∆ CBX. Z

A X Y B

11. Prove that two equilateral triangles having one pair of corresponding sides equal are congruent.

B

12. In ∆ ABC, ∠A = ∠C and BM bisects ∠ABC. Prove that BM
is perpendicular to AC.

A M C

B
13. In the adjoining figure, O is the midpoint
of PQ and ∠A = ∠B. Prove that P O Q
∆ PAO ≅ ∆ QBO.

A
K

14. In the adjoining figure, OD = OS and ∠K = ∠A. D
Prove that ∆ KOD ≅ ∆ AOS.
O
S
A
R T B S
15. In the given figure, ∆ PQR ≅ ∆ TSI and RA, IB are
their respective medians. Prove that RA = IB. Q
P A I

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