Sabrina wants to construct a triangle that will be congruent to δpqr.
which set of actio...
Mathematics, 15.01.2020 23:31 leslieevanessa
Sabrina wants to construct a triangle that will be congruent to δpqr.
which set of actions will not result in a congruent triangle?
translate each of segments pq, pr, and rq by a distance, x. the new triangle will be congruent to δpqr by side-side-side triangle congruence because translations preserve length.
apply a dilation of magnitude 0.5 centered at point p to segments pq, pr, and rq. dilations preserve angle measures and parallel lines. therefore, the new triangle is congruent to δpqr by side-side-side triangle congruence.
reflect point r across segment pq and label the image point r′. construct segments to join p and q to r′; then p and q will be the same distance from r′ as from r. therefore, δpqr′ is congruent to δpqr by side-side-side triangle congruence.
rotate the portion of δpqr consisting of segments pq, pr, and ∠p by 50° around point p. construct the segment whose endpoints are the images of points q and r under the rotation. rotations preserve length and angle measures. therefore, the new triangle is congruent to δpqr by side-angle-side triangle congruence.
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