Math / Geometry

Question3. Kyle says that $\Delta J K L$ is congruent to $\Delta L M J$ by the SSS Congruence Theorem. Ava says that $\Delta J K L$ is congruent to $\triangle L M J$ by the HL. Congruence Theorem. Who is correct? Explain your response.

Studdy Solution

STEP 1

What is this asking? We need to figure out if two triangles are congruent by SSS or HL, and explain why. Watch out! Don't mix up the SSS (Side-Side-Side) and HL (Hypotenuse-Leg) congruence theorems!

STEP 2

1. Analyze the given information
2. Check SSS Congruence
3. Check HL Congruence
4. Determine who is correct

STEP 3

Alright, so we've got two right triangles, $\Delta JKL$ and $\Delta LMJ$ , hanging out in a rectangle.
They share a diagonal, $JL$ .
We're also told that $JK$ and $LM$ are congruent, and $KL$ and $MJ$ are congruent too.
Awesome!

STEP 4

SSS means we need three pairs of congruent sides.
We know $JK \cong LM$ and $KL \cong MJ$ .
Do we have a third pair?

STEP 5

Yes! The triangles share side $JL$ , so $JL \cong JL$ by the reflexive property.
That's our third pair!

STEP 6

So, we have $JK \cong LM$ , $KL \cong MJ$ , and $JL \cong JL$ .
Boom! That's SSS congruence!

STEP 7

HL means we need a congruent hypotenuse and a congruent leg in our right triangles.

STEP 8

The hypotenuse of $\Delta JKL$ is $JL$ , and the hypotenuse of $\Delta LMJ$ is also $JL$ .
So, the hypotenuses are congruent: $JL \cong JL$ .

STEP 9

We also know that $JK \cong LM$ (or $KL \cong MJ$ ), which are pairs of legs.

STEP 10

So we have a congruent hypotenuse and a congruent leg.
That's HL congruence!

STEP 11

Kyle said SSS, and Ava said HL.
We've shown that both are correct!
High five!

STEP 12

Both Kyle and Ava are correct! $\Delta JKL \cong \Delta LMJ$ by both SSS and HL.

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Question3. Kyle says that $\Delta J K L$ is congruent to $\Delta L M J$ by the SSS Congruence Theorem. Ava says that $\Delta J K L$ is congruent to $\triangle L M J$ by the HL. Congruence Theorem. Who is correct? Explain your response.

Studdy Solution

STEP 1

What is this asking? We need to figure out if two triangles are congruent by SSS or HL, and explain why. Watch out! Don't mix up the SSS (Side-Side-Side) and HL (Hypotenuse-Leg) congruence theorems!

STEP 2

1. Analyze the given information
2. Check SSS Congruence
3. Check HL Congruence
4. Determine who is correct

STEP 3

Alright, so we've got two right triangles, $\Delta JKL$ and $\Delta LMJ$ , hanging out in a rectangle.
They share a diagonal, $JL$ .
We're also told that $JK$ and $LM$ are congruent, and $KL$ and $MJ$ are congruent too.
Awesome!

STEP 4

SSS means we need three pairs of congruent sides.
We know $JK \cong LM$ and $KL \cong MJ$ .
Do we have a third pair?

STEP 5

Yes! The triangles share side $JL$ , so $JL \cong JL$ by the reflexive property.
That's our third pair!

STEP 6

So, we have $JK \cong LM$ , $KL \cong MJ$ , and $JL \cong JL$ .
Boom! That's SSS congruence!

STEP 7

HL means we need a congruent hypotenuse and a congruent leg in our right triangles.

STEP 8

The hypotenuse of $\Delta JKL$ is $JL$ , and the hypotenuse of $\Delta LMJ$ is also $JL$ .
So, the hypotenuses are congruent: $JL \cong JL$ .

STEP 9

We also know that $JK \cong LM$ (or $KL \cong MJ$ ), which are pairs of legs.

STEP 10

So we have a congruent hypotenuse and a congruent leg.
That's HL congruence!

STEP 11

Kyle said SSS, and Ava said HL.
We've shown that both are correct!
High five!

STEP 12

Both Kyle and Ava are correct! $\Delta JKL \cong \Delta LMJ$ by both SSS and HL.

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Question3. Kyle says that ΔJKL\Delta J K LΔJKL is congruent to ΔLMJ\Delta L M JΔLMJ by the SSS Congruence Theorem. Ava says that ΔJKL\Delta J K LΔJKL is congruent to △LMJ\triangle L M J△LMJ by the HL. Congruence Theorem. Who is correct? Explain your response.

Studdy Solution

STEP 1

What is this asking? We need to figure out if two triangles are congruent by SSS or HL, and explain why. Watch out! Don't mix up the SSS (Side-Side-Side) and HL (Hypotenuse-Leg) congruence theorems!

STEP 2

1. Analyze the given information2. Check SSS Congruence3. Check HL Congruence4. Determine who is correct

STEP 3

Alright, so we've got two right triangles, ΔJKL\Delta JKLΔJKL and ΔLMJ\Delta LMJΔLMJ, hanging out in a rectangle.They share a diagonal, JLJLJL.We're also told that JKJKJK and LMLMLM are congruent, and KLKLKL and MJMJMJ are congruent too.Awesome!

STEP 4

SSS means we need three pairs of congruent sides.We know JK≅LMJK \cong LMJK≅LM and KL≅MJKL \cong MJKL≅MJ.Do we have a third pair?

STEP 5

Yes! The triangles share side JLJLJL, so JL≅JLJL \cong JLJL≅JL by the **reflexive property**.That's our third pair!

STEP 6

So, we have JK≅LMJK \cong LMJK≅LM, KL≅MJKL \cong MJKL≅MJ, and JL≅JLJL \cong JLJL≅JL.Boom! That's SSS congruence!

STEP 7

HL means we need a congruent hypotenuse and a congruent leg in our right triangles.

STEP 8

The hypotenuse of ΔJKL\Delta JKLΔJKL is JLJLJL, and the hypotenuse of ΔLMJ\Delta LMJΔLMJ is also JLJLJL.So, the hypotenuses are congruent: JL≅JLJL \cong JLJL≅JL.

STEP 9

We also know that JK≅LMJK \cong LMJK≅LM (or KL≅MJKL \cong MJKL≅MJ), which are pairs of legs.

STEP 10

So we have a congruent hypotenuse and a congruent leg.That's HL congruence!

STEP 11

Kyle said SSS, and Ava said HL.We've shown that *both* are correct!High five!

STEP 12

Both Kyle and Ava are correct! ΔJKL≅ΔLMJ\Delta JKL \cong \Delta LMJΔJKL≅ΔLMJ by both SSS and HL.

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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.

Question3. Kyle says that $\Delta J K L$ is congruent to $\Delta L M J$ by the SSS Congruence Theorem. Ava says that $\Delta J K L$ is congruent to $\triangle L M J$ by the HL. Congruence Theorem. Who is correct? Explain your response.

1. Analyze the given information
2. Check SSS Congruence
3. Check HL Congruence
4. Determine who is correct

Alright, so we've got two right triangles, $\Delta JKL$ and $\Delta LMJ$ , hanging out in a rectangle.
They share a diagonal, $JL$ .
We're also told that $JK$ and $LM$ are congruent, and $KL$ and $MJ$ are congruent too.
Awesome!

SSS means we need three pairs of congruent sides.
We know $JK \cong LM$ and $KL \cong MJ$ .
Do we have a third pair?

Yes! The triangles share side $JL$ , so $JL \cong JL$ by the reflexive property.
That's our third pair!

So, we have $JK \cong LM$ , $KL \cong MJ$ , and $JL \cong JL$ .
Boom! That's SSS congruence!

The hypotenuse of $\Delta JKL$ is $JL$ , and the hypotenuse of $\Delta LMJ$ is also $JL$ .
So, the hypotenuses are congruent: $JL \cong JL$ .

We also know that $JK \cong LM$ (or $KL \cong MJ$ ), which are pairs of legs.

So we have a congruent hypotenuse and a congruent leg.
That's HL congruence!

Kyle said SSS, and Ava said HL.
We've shown that both are correct!
High five!

Both Kyle and Ava are correct! $\Delta JKL \cong \Delta LMJ$ by both SSS and HL.