Question

@mathstudent55

Answer 1

G: Triangles DEF and DEG; m Given
2. Definition of Congruent Angles
3. Reflexive Property of Congruence
4. Triangle DEF is similar to Triangle DEG --> Angle-Angle Triangle Similarity Postulate

is that correct?

Answer 2

No.
You need to start with the given info.
The given info here is the angle measures that are shown in the figure.
Then you need to show that two angles of one triangle are congruent to two angles of the other triangle you are proving similar.
Then you use AA similarity as a reason to state that the triangles are congruent.

Answer 3

A two-column proof starts with a two-column set up with statements and reasons.

Answer 4

i know that part

Answer 5

Now I'll just write using text bec it's easier than using the figure, but keep the correct format by using the setup above.

Answer 6

1. m<DEG = 60 deg 1. Given
2. m<EFG = 60 deg 2. Given
3. m<DEG = m<EFG 3. Substitution property of equality
4. \(\angle DEG \cong \angle EFG\) 4. Definition of congruent angles.

Answer 7

That already proved one pair of angles is congruent.
For AA Similarity, we need a second pair of angles.
Do you see another pair of angles, one in one triangle and one in the other triangle that are congruent?

Answer 8

Sometimes, separating the triangles makes it easier to see.

Answer 9

so the proof u wrote on the tope is the anwser?\

Answer 10

Angle F of triangle DEF is congruent to angle E of triangle DGE.
Is there a second pair of congruent angles we can see from the figure?

Answer 11

Are you reading what I am writing?
I have proved one pair of angle congruent.
We need a second pair of angles congruent.
I am waiting for you to read what I wrote and participate.
I am waiting for your answer to go on.

Answer 12

im reading

Answer 13

Great.

Answer 14

is their 3 congruent angles in all?

Answer 15

Remember what we discussed above.
To use AA similarity to prove two triangles similar, you need two pairs of congruent triangles.
The figure showed that two angles measure 60 degrees.
One 60-deg angle is in one triangle, and the other 60-deg angle is in the other triangle.
These two angles, then, can be used as one pair of congruent corresponding angles.
Now we need a second pair of angles, one angle from each triangle, that from looking at the figure, we know for sure are congruent.

Answer 16

so d is congruent to d and from triangle efd e is congruent to g on triangle egd

Answer 17

That is exactly it.
You got it.
This is the key to this problem.

Answer 18

can you just tell me the answer it'd be much appreciated

Answer 19

In geometry, we are not allowed to conclude angles are congruent by the way they look in a figure.
In this case, angle D is an angle of both triangles, so angle D is congruent to angle D, and that is the other pair of corresponding angles that are congruent.

Answer 20

Now we continue with the proof.

Answer 21

k

Answer 22

idk how to do this proof i only know the basics

Answer 23

5. \(m\angle D = m\angle D\) 5. Reflexive property of equality
6. \(\angle D \cong \angle D\) 6. Definition of congruent angles
7. \(\triangle DEF \sim \triangle DGE\) 7. AA similarity

Answer 24

That is the rest of the proof.

Answer 25

thank you very much

Answer 26

Once the two pairs of angles are shown to be congruent, you can use AA similarity to justify that the triangles are similar.

Answer 27

You're welcome.

Answer 28

iv been sitting here for an hour trying to get an anwser to one of my question outof the 135 questions i need to do