CONCEPT PREVIEW Name the corresponding angles and the correspondi...

Question

CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles. 
 (EA is parallel to CD.)

Accepted Answer

Hello, everyone. We are asked to identify the corresponding angles and sides in the pair of similar triangles. Our triangles are Q Pr NTSR. They share the vertex of the angle R we are told side PQ is parallel to side ST So let's see what we can match up and what we know. So if PQ is parallel to ST I'm gonna just mark that on my figure with little arrowheads and then let's see what I know. So I'm gonna start with my angles. So in my angles, I noticed that angle QR P and angle TRS are vertical angles and I recall that vertical angles are equal. So this means we can say the angle, QR P and angle either S RT or we could put S or we could put TRS, those are a pair because of the vertical angles next because alternate interior angles of a transversal that cuts two parallel lines are equal. I can see that angle Q and angle S are a pair. And because we're already told these are similar triangles. If two pairs are similar, I can go ahead and say the angle P and angle T are another pair of angles that match that correspond. So now thinking about my sides, I use the angles to help me find which sides correspond because if they don't have the same number of semicircles or if their angles don't match up, the sides don't match up. So I'm starting with side QR, so QR goes from the two semicircle angle to the one semi circle angle in my drawing. So that would be side sr in the larger triangle. Next, looking at site RP in the smaller triangle that goes from my one semicircle angle to my three semicircle angle. So that would be RT in our larger triangle. And that leaves us with side QP which goes from the my two semicircle angle to my three semicircle angle. So it would correspond with ST in my larger triangle. And that should be all of our angles and sides have a nice day.

CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles. (EA is parallel to CD.)

Key Concepts

Similar Triangles

Corresponding Angles

Parallel Lines and Transversals

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