Geometry / Mr. Hansen	Name: _______________________________________
12/8/2007

Answers to Selected Problems

Warning: For best results, you should peek at these answers only
after attempting the problems on your own, under time pressure.

p. 323 #26.	1. Look at , a right triangle. By the 180° theorem, = (90 – a)°.
	2. Now look at . Again by the 180° theorem, h = 180 – (2a + (90 – a)) = 90 – a.
	3. Now look at . We can see that 2a + b + d = 180, from which 2a = 180 – (b + d).
	4. Solve for a in the result of step 3 to get a = 90 – (b + d)/2.
	5. Substitute the result of step 4 into step 2 to get h = 90 – a = 90 – (90 – (b + d)/2) = (b + d)/2. (Q.E.D.)
	If this problem, or one similar to it, were featured on the test, you would be able to earn considerable partial credit merely by writing the “forward chaining” equations in steps 1 and 2. In other words, you use the only things that you know to apply here, which are that the angles in various triangles must add up to 180°.
	Earning full credit is a bit more challenging, since you have to be able to use your algebra skills in a creative way to solve a problem. This is harder than the problems you saw in Algebra I, where you were told exactly what to do and when to do it. For the next problem, which is a 2-column proof, you should be able to do it, although I agree there are a lot of steps. If the only way you can get a correct solution for the immunity challenge is to copy my work, then so be it; I would prefer that you could do it on your own, but since I am providing a correct solution, I would rather that you copy it (and perhaps learn something in the process) than skip it entirely.
p. 290 #13.	____________________________________________________________________________________
	1.	| 1. Given
	2.	| 2. Given
	3.	| 3. ITT
	4.	| 4. Refl.
	5. Angles PQA and PQB are rt.	| 5. Def.
	6.	| 6. HL (3, 4)
	7.	| 7. CPCTC
	8.	| 8. Refl.
	9. Angles AQR and BQR are rt.	| 9. Def.
	10. Angles AQR and BQR are	| 10. All rt.
	11.	| 11. SAS (7, 10, 8)
	12.	| 12. CPCTC
	13.	| 13. Refl.
	14.	| 14. SSS (3, 12, 13)
	15.	| 15. CPCTC
	(Q.E.D.)