Question

Which statements are true about ΔJKL and ΔLMN? Select all that apply.

Answer 1

Answer:

A. ΔJKL and ΔLMN have only one pair of angles that are congruent

C. ΔJKL has angles that measure

Explanation:

step 1

Find the value of x

we know that

----> by vertical angles

substitute the given values

solve for x

step 2

Find the measure of the interior angles of triangle JKL

we have

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

therefore

Triangle JKL has angles that measure

step 3

Find the measure of the interior angles of triangle LMN

we have

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

Triangle LMN has angles that measure

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The corresponding angles of triangle JKL and LMN are not congruent

therefore

The triangles are not similar

Verify each statement

Part a) ΔJKL and ΔLMN have only one pair of angles that are congruent

The statement is true (see the explanation)

Part b) ΔJKL and ΔLMN have two pairs of angles that are congruent

The statement is false

Because have only one pair of angles that are congruent

Part c) ΔJKL has angles that measure

The statement is true (see the explanation)

Part d) ΔLMN has angles that measure

The statement is false

Because, Triangle LMN has angles that measure

Part e) ΔJKL and ΔLMN are similar

The statement is false

Because, the corresponding angles are not congruent

Explanation:

Answer 2

A. ΔJKL and ΔLMN have only one pair of angles that are congruent

C. ΔJKL has angles that measure
`50^o,60^o,70^o`

Explanation:

step 1

Find the value of x

we know that

`m\angle KLJ=m\angle MLN` ----> by vertical angles

substitute the given values

`(6x-2)^o=(5x+10)^o`

solve for x

`6x-5x=10+2\\x=12`

step 2

Find the measure of the interior angles of triangle JKL

we have

`m\angle KLJ=(6(12)-2)=70^o`

`m\angle KJL=(5(12))=60^o`

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

`m\angle JKL=180^o-130^o=50^o`

therefore

Triangle JKL has angles that measure
`50^o,60^o,70^o`

step 3

Find the measure of the interior angles of triangle LMN

we have

`m\angle MLN=(5(12)+10)=70^o`

`m\angle LMN=(6(12)-7)=65^o`

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

`m\angle LNM=180^o-135^o=45^o`

Triangle LMN has angles that measure
`45^o,65^o,70^o`

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The corresponding angles of triangle JKL and LMN are not congruent

therefore

The triangles are not similar

Verify each statement

Part a) ΔJKL and ΔLMN have only one pair of angles that are congruent

The statement is true (see the explanation)

Part b) ΔJKL and ΔLMN have two pairs of angles that are congruent

The statement is false

Because have only one pair of angles that are congruent

Part c) ΔJKL has angles that measure
`50^o,60^o,70^o`

The statement is true (see the explanation)

Part d) ΔLMN has angles that measure
`50^o,60^o,70^o`

The statement is false

Because, Triangle LMN has angles that measure
`45^o,65^o,70^o`

Part e) ΔJKL and ΔLMN are similar

The statement is false

Because, the corresponding angles are not congruent