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. 
 (HK is parallel to EF.)​​

Accepted Answer

Hello, everyone. We are asked to identify the corresponding angles and sides in a pair of similar triangles. We are given triangle MNO and triangle PQO, the triangles meet at the 0.0 we are told side MN is paralleled side PQ. So I'm gonna draw a little arrowhead on MN and PQ just to show they are parallel from there. I recognize that they meet at 0.0. So this will give us our first set of ma matching angles or corresponding angles because Engle Mon would be a vertical angle with angle POQ. So they would be congruent. So they would be corresponding in this case. So angle mon and angle Poq are our first set of matching angles. Our next set of corresponding angles. If I know MN is parallel to PQ, then segment PN would be a transversal cutting them. And there's a rule that says alternate interior angles of parallel lines cut by a transversal are congruent. So I'm putting two semicircles on angle N and it's gonna be corresponding to angle P. And since we know they are similar, we can go ahead and say that the angle at M corresponds to the angle at Q and I put semicircles there just to match them up. So now looking for my corresponding sides, I'm gonna match up the sides between corresponding angles. So I am gonna start with side on, on goes from my one semi circled angle to my two semi circled angle. And in the larger triangle that would be side op Next, I'm gonna look at om om goes from my one semicircle angle to my three semicircle angle. And on my other triangle, that would be the side OQ. So that leaves side and M and that goes from N which is my two semicircles to M which has three. So on the other triangle, it would be from P to Q. So side nm would be corresponding to side PQ and we now have three corresponding sets of angles and sides. So we have them all labeled, have a nice day.

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

Key Concepts

Similar Triangles

Corresponding Angles

Parallel Lines

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