For each pair of triangles,tell:(a) are they congruent(b)write the triangle congruency statement.(c) Give the postulate that makes them congruent.

All right...before we begin, let's lay some ground rules about the postulate your teacher asks for in every problem. If you already know what they are, skip this paragraph...

A postulate is a statement that claims how the triangles are congruent from looking at the paper. For example, on number 2 we have three sides of the triangle so we would use the postulate SSS (side, side, side). However, number one we would use SAS (side, angle, side) because we see the angle square showing it is a 90-degree angle.
Let's begin! (I haven't done triangles in a while so I apologize in advance if some of my answers might be incorrect on the congruent (yes or no) part of it.)

1.
A) From a visual perspective, we can see the triangles are congruent.
B) ABE = CDE because they are the corresponding points.
C) We can use SAS for the postulate.

2.
A) Yes, they are congruent.
B) OLE = OVE
C) We can use SSS for their postulate.

3.
A) Yes, they are congruent.
B) AWT = ERT
C) We can use SAS for the postulate.

4.
A) I believe the triangles are congruent. You might want to check me on that.
B) GFE = FGH
C) SSS

5.
A) They are congruent because if IH bisects it, it is directly in the middle. So, we know that WH = HS and IH = IH (duh.) and their angles match.
B) WHI = SHI
C) SAS

6.
A) This one is intriguing because it would state above the shape "LE bisects LGUE." I'm going to take that it isn't exactly in the middle, but I am still going to say it is congruent.
B) LGE = EUL
C) ASA

7.
A) Yes, they are definitely congruent.
B) RTU = TRS
C) SSS (We have nothing that indicates angles.)

8.
A) Yes, they are congruent.
B) YWV = VZY
C) We can use SAS. (Might want to check that one.)

9.
A) I would say this one is NOT congruent.
B) There are only two points. One way is HT = MA
C) They are not congruent, you can not use a postulate. However, if you teacher insists on putting one, I would use SAS.

Once again, I would be careful about my answers. I haven't worked with triangles in a few years. If my math is incorrect, or I didn't give the answer you were looking for, please let me know. However, if my math is on point, please consider marking as Brainliest.

Have a good one.
God Bless.

jainveenamrata jainveenamrata · Answer 2 · 2022-01-25T03:02:09-05:00

They both are congruent to each other.

Congruency of triangles.

In triangles, if their corresponding sides and angles are equal then the triangle is congruent.

Step by step explanation

a) In \(\Delta ECD\ and\ \Delta EAB\\\)

\(\begin{aligned} \angle DEC &= \angle BEA\ (vertically\ opposite\ angle)\\ AC &= EC\ (given)\\ \angle C &= \angle A = 90^{o} \end{aligned}\)

Hence, Both the triangles are congruent to each other.

b) In \(\Delta OEL\ and\ \Delta OEV\)

\(\begin{aligned} OL &= OV (given)\\ LE &= VE\ (given)\\ OE &= OE\ (common\ side) \end{aligned}\)

Hence, Both the triangles are congruent to each other.

c) To show the congruency in the triangle we need to follow the condition.

1. All sides are equal

2. one side and two angles

3. one angle and two sides

Thus, they are congruent to each other.

To know more about the congruency of triangles link is given below.

https://brainly.com/question/19258025