Right Triangles

and Similarity

Problems

Solved


 

1. Use a paragraph proof to prove the similarity theorem. Use your gsp sketches and measures to help you.

We are given that PQR is a right angle and that segment QS is an altitude of PQR. We want to show that

PSQ is similar to PQR; PQR is similar to QSR ; PSQ is similar to QSR.

Proof:

PQR is a right angle and segment QS is an altitude, so segment QS is perpendicular to segment RP. Thus PSQ and RSQ are right angles by the definition of perpendicular lines. Therefore PSQ PQR and RSQ PQR since right angles are congruent. Since congruence of angles is reflexive we have SPQ SPQ and SRQ SRQ. Therefore by AA similarity we have PSQ is similar to PQR; PQR is similar to QSR. Since similarity is transitive we also have PSQ is similar to QSR.

 

2. Click on the GSP sketch and follow the instructions. Then answer the following:

Using the figure to the right, name the three similar triangles

EAB is similar to AFB

EAB is similar to EFA

AFB is similar to EFA

3.4. 5. 6.


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