- x= 40.From the last question, you know the ratio between similar
triangles OQR and OMN is 2:1. That ratio means that a line
segment in the smaller triangle is half the size of the corresponding
line segment in the larger triangle. If that line segment measures
20 inches, it is half the size of the corresponding line segment.
Create the equation: 20 = ^12 x. x= 40.
Set 35
- ΔWXY and ΔAYB.(Remember to align corresponding vertices.)
- AB= 4. Since WYAB, set up the proportion:
WXYY= YABB, ^1162 = A 3 B
Since YBis ^14 the length of XY, ABwill be ^14 the length of WY.
^14 of 16 is 4, so AB= 4.- Angle-Angle postulate.Since there are no side measurements to
compare, only an all-angular postulate can prove triangle similarity. - XYacts like a transversal across WXand BY. When alternate
interior angles are congruent, then lines are parallel. In this case,
∠WXY and ∠BYA are congruent alternate interior angles. WX
and BYare parallel.
Set 36
- ΔAEC and ΔBDC.(Remember to align corresponding vertices.)
- Corresponding line segments are AEand BD; ECand DC;
CAand CB.Always coordinate corresponding endpoints. - Angle-Angle postulate.Though it is easy to overlook, vertex C
applies to both triangles.
501 Geometry Questions