Question

if m is the mid point of ab in rectangle ABCD prove that triangle ABD is congruent to BMC

Answer 1

Given:

In rectangle ABCD AB=2BC and if M is the midpoint of AB in rectangle ABCD

To Find:

prove that triangle AMD is congruent to BMC

Solution:

Let us construct a rectangle ABCD and name the length BC as 'a' and length AB as '2a' because it is given that AB=2BC, Now we will consider the triangles AMD and BMC, from these triangles we get that,

$AM=BM=a$

$AD=BC=a$

$\angle MAD=\angle MBC=90^{\circ}$

So from the SAS(side angle side ) congruency theorem, we can state that,

$\bigtriangleup AMD\cong \bigtriangleup BMC$

Using side angle side congruency theorem these triangles are congruent, we could also use SSS( side side side ) congruency theorem and find the values of MD and MC which will come to be equal and so will be congruent

Hence, proved that triangle AMD is congruent to BMC.

Right Question:

In rectangle ABCD AB=2BC and if M is the midpoint of AB in rectangle ABCD prove that triangle AMD is congruent to BMC

Answer 2

Step-by-step explanation:

given

ABCD is a rectangle M is the mid point of AB

1. To prove ∆AMB is congreunt to ∆BMC
2. proof In ∆AMD and BMC
3. AM=bm. a