triangle ABC with A at 0 comma 0, B at 2 comma 4 and C at 0 comma 2, the measure of angle C is 135 degrees, and the measure of angle B is 30 degrees, triangle DEF with D at 2 comma 0, E at 4 comma 4 and F at 4 comma 2, the measure of angle F is 135 degrees, and the measure of angle D is 30 degrees Name the congruent triangles and justify the reason for congruence

by SSS congruence.

Step-by-step explanation:

Given the two triangles with following coordinates and angles:

A(0, 0)

B(2, 4)

C(0, 2)

D(2, 0)

E(4, 4)

F(4, 2)

Let us calculate the sides of the two triangles one by one.

Distance formula:

and are the two coordinates of which distance is to be calculated.

Sides AB = DE

BC = DF and

AC = EF

All the three sides are equal here. So SSS (Side Side Side) congruence.

And angles:

Therefore,

by SSS congruence.

answer:      

step-by-step explanation:

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.