Question

In the figure, point B is the midpoint of AC . Use the figure to answer the questions.

Answer 1

Answer

Proof of (a)

Disagree with the  ΔABD = ΔCBD by the SAS congruence postulate .

SAS congurence property

In this congurence property two sides and one angle of the two triangles are equal .

(1) BD = BD ( Common sides of the  ΔABD and ΔCBD )

(2) AB =BC (B is the midpoint of the AC i.e it bisect AC in the two equal parts.)

but equal angles are not given

therefore disagree with the  ΔABD = ΔCBD  by the SAS congurence postulate .

Proof of (b)

SSS congurence property

In this congurence property three sides of the two triangles are equal .

In the ΔABD and ΔCBD .

(1) BD = BD ( Common sides of the  ΔABD and ΔCBD )

(2) AB =BC (B is the midpoint of the AC i.e it bisect AC in the two equal parts.)

(3) AD=CD  (Given )

ΔABD = ΔCBD  by the SSS congurence theorem

Hence proved