- ΔJ.The three angles in ΔE measure 36°, 54°, and 90°. ΔF and ΔJ
also have angles that measure 36°, 54°, and 90°. According to the
Angle-Angle postulate, at least two congruent angles prove sim-
ilarity. To be congruent, an included side must also be congruent.
The line segments between the 36° and 90° angles in ΔJ and ΔE
are congruent.
- ΔF.ΔF has the same right scalene shape as ΔE, but they are not
congruent; they are only similar.
- ΔL. The three angles in ΔD respectively measure 62°, 10°, and
108°. ΔL has a set of corresponding and congruent angles, which
proves similarity; but ΔL also has an included congruent side,
which proves congruency.
- ΔG. ΔG has only one given angle; the Side-Angle-Side postulate
proves it is similar to ΔD. The sides on either side of the 108°
angle are proportional and the included angle is obviously
congruent.
- m= 2.5. Since ΔI ≈ΔA, set up the following proportion to solve
for m, which pairs the two sides opposite the 90°angles and the
two sides that are opposite the 30°angles:
^2100 = m^5
Mwill be ^14 of 10, so (^14 )×10 = ^140 = 2.5.
- r= 6.2. Since ΔF ≈ΔE, set up the following proportion which
pairs up the two sides that are opposite the 90°angles and the two
sides that are opposite the 54°angles:
1120 .4= ^5 r
Since ΔE is half as big as ΔF, rwill be equal to 6.2.
501 Geometry Questions
