Question

in the given figure angle 1 equal to angle 2 and angle 3 equal to angle 4 then prove that BC equal to CD

Answer 1

Answer is attached

Hope it helps

Answer 2

Answer:

By applying the ASA congruency rule to triangles ABC & ADC we can prove that BC = CD.

Step-by-step explanation:

Given: ABCD is a quadrilateral where

<1  =  <2

<3  =  <4

To prove: BC = CD

Proof:

In Δ ABC and ΔADC,

<1 = <2     (given)

<3 = <4    (given)

AC = AC   (common side)

Thus, By ASA Congruency rule,

Δ ABC ≅ ΔADC,

By C.P.C.T(corresponding Parts of Congruent Triangles)

BC = CD

Hence, proved.

Four Congruency Rules:

SAS: If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

ASA: Two triangles are said to be congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle

SSS: In two triangles, if the three sides of one triangle are equal to the corresponding three sides (SSS) of the other triangle, then the two triangles are congruent.

RHS: In two right-angled triangles, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.