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1 answer:
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Answer:
A. ΔJKL and ΔLMN have only one pair of angles that are congruent
C. ΔJKL has angles that measure
Step-by-step 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
<u><em>Verify each statement</em></u>
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