Math / Geometry

QuestionWhich of the following describes the relationship between the given triangles? None of these $\triangle C M N \cong \triangle P A B$ by the AAA congruence theorem $\triangle M C N \cong \triangle P A B$ by the HL congruence theorem $\triangle C M N \cong \triangle A P B$ by the AAS congruence theorem Submit Purerts Fardbark Questions? Abcut Careers Terms of Service PRINACY POLCY Contact Us

Studdy Solution

STEP 1

What is this asking? Which theorem, if any, proves that the two triangles are the same? Watch out! The order of the letters in the triangle names matters!
It tells us which angles and sides match up.

STEP 2

1. Check what we know
2. Explore AAA
3. Explore HL
4. Explore AAS
5. Find the match

STEP 3

Alright, awesome students!
Let's decode this triangle puzzle!
We've got two triangles, and we need to figure out if they're congruent, meaning exactly the same, just maybe rotated or flipped.

STEP 4

From the image, we see $\angle C \cong \angle A$ , $\angle M \cong \angle P$ , and $\angle N \cong \angle B$ .
Remember, those matching arc symbols in the angles tell us they're congruent!

STEP 5

AAA stands for Angle-Angle-Angle.
If all three angles of one triangle are congruent to all three angles of another triangle, are they congruent?

STEP 6

Not necessarily!
Imagine a tiny triangle and a giant triangle, both with the same angles.
They're similar, but not congruent.
So, AAA doesn't prove congruence.

STEP 7

HL stands for Hypotenuse-Leg.
This only works for right triangles.
Do we have right triangles?
Nope! So, HL is out.

STEP 8

AAS stands for Angle-Angle-Side.
If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

STEP 9

Let's see.
We know $\angle C \cong \angle A$ and $\angle M \cong \angle P$ .
We don't have any information about the sides.
So, we can't use AAS yet.

STEP 10

We know all three corresponding angles are congruent.
That means the triangles are similar, but not necessarily congruent.
We don't have enough information to prove congruence.

STEP 11

Let's look at the options. $\triangle CMN \cong \triangle PAB$ by AAA?
Nope, AAA doesn't prove congruence. $\triangle MCN \cong \triangle PAB$ by HL?
Nope, not right triangles. $\triangle CMN \cong \triangle APB$ by AAS?
Nope, we don't know about any sides.

STEP 12

None of these options work!
We don't have enough information to say the triangles are congruent.

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Studdy Solution

STEP 1

What is this asking? Which theorem, if any, proves that the two triangles are the same? Watch out! The order of the letters in the triangle names matters!
It tells us which angles and sides match up.

STEP 2

1. Check what we know
2. Explore AAA
3. Explore HL
4. Explore AAS
5. Find the match

STEP 3

Alright, awesome students!
Let's decode this triangle puzzle!
We've got two triangles, and we need to figure out if they're congruent, meaning exactly the same, just maybe rotated or flipped.

STEP 4

From the image, we see $\angle C \cong \angle A$ , $\angle M \cong \angle P$ , and $\angle N \cong \angle B$ .
Remember, those matching arc symbols in the angles tell us they're congruent!

STEP 5

AAA stands for Angle-Angle-Angle.
If all three angles of one triangle are congruent to all three angles of another triangle, are they congruent?

STEP 6

Not necessarily!
Imagine a tiny triangle and a giant triangle, both with the same angles.
They're similar, but not congruent.
So, AAA doesn't prove congruence.

STEP 7

HL stands for Hypotenuse-Leg.
This only works for right triangles.
Do we have right triangles?
Nope! So, HL is out.

STEP 8

AAS stands for Angle-Angle-Side.
If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

STEP 9

Let's see.
We know $\angle C \cong \angle A$ and $\angle M \cong \angle P$ .
We don't have any information about the sides.
So, we can't use AAS yet.

STEP 10

We know all three corresponding angles are congruent.
That means the triangles are similar, but not necessarily congruent.
We don't have enough information to prove congruence.

STEP 11

Let's look at the options. $\triangle CMN \cong \triangle PAB$ by AAA?
Nope, AAA doesn't prove congruence. $\triangle MCN \cong \triangle PAB$ by HL?
Nope, not right triangles. $\triangle CMN \cong \triangle APB$ by AAS?
Nope, we don't know about any sides.

STEP 12

None of these options work!
We don't have enough information to say the triangles are congruent.

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Studdy Solution

STEP 1

What is this asking? Which theorem, if any, proves that the two triangles are the same? Watch out! The order of the letters in the triangle names matters!It tells us which angles and sides match up.

STEP 2

1. Check what we know2. Explore AAA3. Explore HL4. Explore AAS5. Find the match

STEP 3

Alright, awesome students!Let's **decode** this triangle puzzle!We've got two triangles, and we need to figure out if they're **congruent**, meaning *exactly* the same, just maybe rotated or flipped.

STEP 4

From the image, we see ∠C≅∠A\angle C \cong \angle A∠C≅∠A, ∠M≅∠P\angle M \cong \angle P∠M≅∠P, and ∠N≅∠B\angle N \cong \angle B∠N≅∠B.Remember, those matching arc symbols in the angles tell us they're **congruent**!

STEP 5

AAA stands for **Angle-Angle-Angle**.If all three angles of one triangle are congruent to all three angles of another triangle, are they congruent?

STEP 6

Not necessarily!Imagine a tiny triangle and a giant triangle, both with the same angles.They're similar, but not congruent.So, **AAA doesn't prove congruence**.

STEP 7

HL stands for **Hypotenuse-Leg**.This only works for *right* triangles.Do we have right triangles?Nope! So, **HL is out**.

STEP 8

AAS stands for **Angle-Angle-Side**.If two angles and a *non-included* side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

STEP 9

Let's see.We know ∠C≅∠A\angle C \cong \angle A∠C≅∠A and ∠M≅∠P\angle M \cong \angle P∠M≅∠P.We don't have any information about the sides.So, we can't use **AAS** yet.

STEP 10

We know all three corresponding angles are congruent.That means the triangles are *similar*, but not necessarily *congruent*.We don't have enough information to prove congruence.

STEP 11

STEP 12

None of these options work!We don't have enough information to say the triangles are congruent.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Which theorem, if any, proves that the two triangles are the same? Watch out! The order of the letters in the triangle names matters!
It tells us which angles and sides match up.

1. Check what we know
2. Explore AAA
3. Explore HL
4. Explore AAS
5. Find the match

Alright, awesome students!
Let's decode this triangle puzzle!
We've got two triangles, and we need to figure out if they're congruent, meaning exactly the same, just maybe rotated or flipped.

From the image, we see $\angle C \cong \angle A$ , $\angle M \cong \angle P$ , and $\angle N \cong \angle B$ .
Remember, those matching arc symbols in the angles tell us they're congruent!

AAA stands for Angle-Angle-Angle.
If all three angles of one triangle are congruent to all three angles of another triangle, are they congruent?

Not necessarily!
Imagine a tiny triangle and a giant triangle, both with the same angles.
They're similar, but not congruent.
So, AAA doesn't prove congruence.

HL stands for Hypotenuse-Leg.
This only works for right triangles.
Do we have right triangles?
Nope! So, HL is out.

AAS stands for Angle-Angle-Side.
If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Let's see.
We know $\angle C \cong \angle A$ and $\angle M \cong \angle P$ .
We don't have any information about the sides.
So, we can't use AAS yet.

We know all three corresponding angles are congruent.
That means the triangles are similar, but not necessarily congruent.
We don't have enough information to prove congruence.

None of these options work!
We don't have enough information to say the triangles are congruent.