Page 192 - Start Up Mathematics_7

P D

2.5 cm 2.5 cm
(a) 6 cm 6 cm
90°
90°
Q R F E

B

C D 90° 4.1 cm

90° 90°
(b) 3 cm 3 cm (c) C A

A 5 cm B
90° 4.1 cm

D
Solution: (a) In ∆ PQR and ∆ DEF
∠Q = ∠E (each 90°)

PR = DF (each 6 cm)
PQ = DE (each 2.5 cm)
∆ PQR  ∆ DEF (by RHS congruence criterion)

(b) In ∆ ABC and ∆ BAD
∠C = ∠D (each 90°)

AC = BD (each 3 cm)
AB = BA (common hypotenuse)

∆ ABC  ∆ BAD (by RHS congruence criterion)
(c) In ∆ ABC and ∆ ADC

∠B = ∠D (each 90°)
AB = AD (each 4.1 cm)
AC = AC (common hypotenuse)

∆ ABC  ∆ ADC (by RHS congruence criterion)

Example 16: ∆ ABC is isosceles in which AB = AC and AD is one of A
its altitudes.
(a) State any three pairs of equal parts in ∆ ADB and
∆ ADC.

(b) Is ∆ ADB  ∆ ADC? If yes, mention the criteria used.
(c) Is BD = CD? Why or why not?

(d) Is ∠BAD = ∠CAD? Why or why not? B D C

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