Question

In the figure angle CAB equals to angle BDC angle ACB equals to angle DBC prove that AB equal to DC and AC equals to BD.​

Answer 1

Question:

In the figure angle CAB equals to angle BDC angle ACB equals to angle DBC prove that AB equal to DC and AC equals to BD.

To prove?

• AB=DC
• AC=BD

Answer:

First we have to prove △ABC congurent to △BDC

In triangle △ABC and △BDC

• ∠A=∠D(angle)

reason:

Given

• ∠ACB=∠DBC(angle)

reason :

Given

• BC=BC(side)

reason :

common side

.°.△ABC ≅△BDC(By ASA)

Now Let's prove AB=DC

As two triangles are congruent by method of Angle side angle

.°. AB=DC (C.P.C.T)

Now Let's prove AC=BD

As two triangles are congruent by method of Angle side angle

.°. AC=BD (C.P.C.T)

HENCE PROVED!

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Understanding concepts to solve such questions:

☆What are congruent triangles☆

•Two triangles are said to be congruent when they have exactly same shape and size.

☆How we can say triangles are congruent☆

•There are four ways to prove two triangles as congruent.

• When three pairs of sides are equal.

We represent it by-->SSS (Side Side Side)

• When two pairs of side and their angles are equal

We represent it by-->SAS (Side Angle Side)

• When two angles and the side between them are equal

We represent it by-->ASA (Angle Side Angle)

• When two angles and the side not between them are equal

We represent it by-->AAS (Angle Angle Side)