23. Which is false? AB is bisector of ZA and AC = AD. Then.
1 2
B.
D
(a) BC = BD
(b)/C=D
(c) AB I CD
(d) AACD must be a right triangle
Answers
Given : AB is angle bisector of ∠ A formed by AC & AD and AC = AD
To find : Which is false
(a) BC = BD
(b) ∠C = ∠D
(c) AB ⊥ CD
(d) AACD must be a right triangle
Solution:
Compare Δ ABC & ΔABD
AB = AB common
∠BAC = ∠BAD ( as AB is angle bisector of ∠ A)
AC = AD given
=> Δ ABC ≅ ΔABD
=> BC = BD - option a is TRUE
∠C = ∠D - option b is TRUE
∠ABD = ∠ABC
∠ABD + ∠ABC = 180° linear pair
=> ∠ABD = ∠ABC = 90°
=> AB ⊥ CD option c is TRUE
∠ACD = ∠ACB
in Δ ABC ∠ABC = 90°
Hence other two angles must be less than 90°
=> ∠ACB < 90°
=> ∠ACD < 90° similarly ∠ADC < 90°
∠CAD = 90° only if ∠ACD = ∠ADC = 45°
Hence ACD must be a right triangle is FALSE
ACD must be a right triangle is FALSE
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Answer:
D
Step-by-step explanation:
AACD MUST BE A RIGHT TRIANGLE