Answers
Set 33
- a.The angles of a right isosceles triangle always measure 45° – 45°
- 90°. Since at least two corresponding angles are congruent, right
isosceles triangles are similar.- b.A ratio is a comparison. If one side of a triangle measures 16
inches, and a corresponding side in another triangle measures 24
inches, then the ratio is 16:24. This ratio can be simplified by
dividing each side of the ratio by the common factor 8. The
comparison now reads, 2:3 or 2 to 3.Choices a, c, and dsimplify
into the same incorrect ratio of 2:1 or 1:2. - d.When writing a proportion, corresponding parts must parallel
each other. The proportions in choices band care misaligned.
Choice alooks for the line segment 20 – x, not x. - d.First, state the ratio between similar triangles; that ratio is 10:2
or 5:1. The ratio means that a line segment in the larger triangle is
always 5 times more than the corresponding line segment in a
similar triangle. If the line segment measures 30 inches, it is 5
times more than the corresponding line segment. Create the
equation: 30 = 5x. x= 6.
Set 34
- ΔOQR and ΔOMN.(Remember to align corresponding vertices.)
- Corresponding line segments are OQand OM; QRand MN;
ROand NO.Always coordinate corresponding endpoints. - Side-Angle-Side.The sides of similar triangles are not congruent;
they are proportional. If the ratio between corresponding line-
segments, ROand NOis 22:11, or 2:1, and the ratio between
corresponding line segments QOand MOis also 2:1, they are
proportional.
501 Geometry Questions