Set 41
- a= 2.SU+ UV= ZY. SU= UV. Since SU= 1 as demonstrated in
question 204, ZY = 1 + 1 = 2. - Acute.ΔZSY is an isosceles triangle. Two of its sides measure
5 2 . The third side measures 2. Plug the given measures into the
Pythagorean theorem. 2^2 + (5 2 )^2 = (5 2 )^2. Thus, 4 + 50 = 50;
54 > 50. Therefore, ΔZSY is acute.
Set 42
- x= 13.Even though you don’t know the measurement of xin
ΔABF, you do know that two sides measure x. Plug the measure-
ments of ΔABF into the Pythagorean theorem. x^2 + x^2 = (13 2 )^2.
2 x^2 = 338. x^2 = 169. x= 13. - AG =^162 ^9. Since AG≅BGand ∠AGB = 90°, plug “a” into the
Pythagorean theorem for both legs: a^2 + a^2 = 13^2 , 2a^2 = 169,
a= ^162 ^9. - 26 2 + 2. The ratio between corresponding line segments AEand
FEis 13 2 + 1:1. Since FD= 2, AC is twice the size of AE.
Set 43
- ΔAFE and ΔBGE are congruent (Side-Side-Side postulate).
ΔABF and ΔBCG are congruent (Side-Side-Side postulate). - w= 21.Plug the measurements of ΔECD into the Pythagorean
theorem: 3^2 + w^2 = (15 2 )^2. 9 + w^2 = 450. w^2 = 441. w= 21. - x= 7.Corresponding parts of congruent triangles are congruent
(CPCTC). If ECis 21, then EAis also 21. Plug the measurements
of ΔAFE into the Pythagorean theorem: 21^2 + x^2 = (7 10 )^2.
441 + x^2 = 490. x^2 = 49. x= 7. - y= 14.Because of CPCTC, AEis also congruent to BE. If BEis
21 and FEis 7, subtract 7 from 21 to find BF. 21 – 7 = 14.
501 Geometry Questions