Question

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Which method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate?


A. Use a rigid transformation to prove ∠NOP ≅ ∠NML.

B. Use a rigid transformation to prove ∠NOP ≅ ∠ONP.

C. Use rigid and nonrigid transformations to prove segment LN over segment ON = segment PN over segment MN.

D. Use rigid and nonrigid transformations to prove segment LM over segment ON = segment PN over segment MN.

Answer 1

Given:

ΔONP and ΔMNL.

To find:

The method and additional information that will prove ΔONP and ΔMNL similar by the AA similarity postulate?

Solution:

According to AA similarity postulate, two triangles are similar if their two corresponding angles are congruent.

In ΔONP and ΔMNL,

$\angle ONP\cong \angle MNL$       (Vertically opposite angles)

To prove ΔONP and ΔMNL similar by the AA similarity postulate, we need one more pair of corresponding congruent angles.

Using a rigid transformation, we can prove

$\angle NOP\cong \angle NML$

Since two corresponding angles are congruent in ΔONP and ΔMNL, therefore,

$\Delta ONP\sim \Delta MNL$        (AA postulate)

Therefore, the correct option is A.

Answer 2

Similar triangles may or may not be congruent.

The additional information to prove ΔONP and ΔMNL are similar by AA similarity postulate is (a) Use a rigid transformation to prove ∠NOP ≅ ∠NML.

From the question, we have:

$\mathbf{\triangle ONP \sim \triangle MNL}$ --- ONP and MNL are similar triangles

Because the similarities of the triangles are to be proved by AA postulate, the following angles must be corresponding and congruent

$\mathbf{\angle ONP \cong \angle MNL}$

$\mathbf{\angle NOP \cong \angle NML}$

$\mathbf{\angle PON \cong \angle LMN}$

Option (b) is incorrect because angles NOP and ONP are not corresponding angles

Options (c) and (d) are incorrect, because they prove the similarities by lines segments.

Hence, the correct option is (a).

This is so because, it proves the similarities of both triangles by using corresponding angles.

Read more about similar triangles at:

https://brainly.com/question/20502441