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In the diagram below, \overline{OH} OH start overline, O, H, end overline is parallel to \overline{ID} ID start overline, I, D, end overline. Find the length of \overline{HD} HD start overline, H, D, end overline.

Respuesta :

Answer:

HP=11

Step-by-step explanation:

Now that we have \blueE{HP}HPstart color #0c7f99, H, P, end color #0c7f99, we can find HDHDH, D.

\begin{aligned} HD&=\blueE{HP}+DP \\\\ &=\blueE{2}+9 \\\\ &=11 \end{aligned}

HD

​

 

=HP+DP

=2+9

=11

​

akposevictor

Using the AAA similarity theorem, the length of segment HD in the diagram given is: 11 units.

What is the AAA Similarity Theorem?

If all corresponding angles of two  triangles are congruent, then, they are similar triangles, based on the AAA similarity theorem.

ΔPOH ~ ΔPID by AAA similarity theorem.

Therefore, their corresponding sides would be proportional. Thus:

PH/PD = PO/PI

Substitute

PH/9 = 6/27

PH = (9 × 6)/27

PH = 2

HD = 2 + 9

HD = 11 units.

Learn more about the AAA similarity theorem on:

https://brainly.com/question/2063552

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