Question

5. Select all the statements that are true about AJKL and ALMN. (20 pts) The have only one pair of congruent angles. They have two pairs of congruent angles. AJKL has angles 50°, 60°, and 70°. ALMN has angles 50°, 60°, and 70°. AJKL and ALMN are similar.

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Answer 1

Step-by-step explanation: A. ΔJKL and ΔLMN have only one pair of angles that are congruent

C. ΔJKL has angles that measure

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