Geometry / Mr. Hansen 9/23/2004

Name: __________KEY___________

Answers to Chapter 1 Review Problems

	Instructions: Please attempt each problem before looking at the answer. Note that most of the odd-numbered answers are on p.750.
2.	Only ÐDEF (straight) can be assumed. Others appear to be (a) right, (b) obtuse, (c) acute, (d) straight, (e) right.
4.(a)	46°52¢30²
(b)	132.1°
6.(a)	No, since mÐ1 > 70.
(b)	Yes.
8.	x + 3x + 2x = 180
	6x = 180
	x = 30
	\ mÐ1 = 30 Ù mÐ2 = 3x = 90 Ù mÐ3 = 2x = 60
10.	1. Given 2. Diag. 3. Diag. 4. Theorem: All str. Ðs are @ (Q.E.D.)
11.	1. Given 2. Given 3. Ð subtr. 4. Def. acute Ð (Q.E.D.)

12.	_____________________________________________________________________________________
	1. ÐX is rt.	| 1. Given
		|
	2. ÐY is rt.	| 2. Given
		|
	3. ÐX @ ÐY	| 3. Theorem: All rt. Ðs are @
	Q.E.D.

13.	_____________________________________________________________________________________
	1.	| 1. Given
		|
	2. A, B, C are collinear	| 2. Diag.
		|
	3.	| 3. Def. collinearity
		|
	4. B is mdpt. of	| 4. Def. mdpt.
	Q.E.D.

14.	_____________________________________________________________________________________
	1. rays DF and DG trisect ÐEDH	| 1. Given
		|
	2. ÐEDF @ ÐFDG @ ÐGDH	| 2. Def. trisection
	Q.E.D.

15.	_____________________________________________________________________________________
	1. ray TW bisects ÐVTX	| 1. Given
		|
	2. ÐVTW @ ÐXTW	| 2. Def. bisection
	Q.E.D.

16.	Since 0.6 = 3/5, 31.6° = (31 3/5)°. Therefore, the angles have the same measure. (Q.E.D.)
20.	40.2° = 40° + (.2)(60¢) = 40°12¢ = 39°72¢ \40.2°/3 = 39°72¢/3 = 13°24¢
22.	Converse: If the angle formed by the hands of a clock is acute, then the time is 2:00. FALSE. Inverse: If the time is not 2:00, then the angle formed by the hands of a clock is not acute. FALSE. Contrapositive: If the angle formed by the hands of a clock is not acute, then the time is not 2:00. TRUE. Warning: Although in this problem, the original statement and its contrapositive were both true, while the converse and inverse were both false, that is not true in general. All you can say in general is that an original statement and its contrapositive are equivalent to each other, and the converse and inverse are equivalent to each other. (The word “equivalent” means “same truth value.”) Therefore, there are 4 possible patterns, numbered i through iv in the table below:
	Original statement	Converse	Inverse	Contrapositive
i	T	T	T	T
ii	T	F	F	T
iii	F	T	T	F
iv	F	F	F	F
26.	Let a = mÐA, b = mÐB. \a = 6 + 2b (given). Substitute that value for a into the other known fact (namely, a + b = 42) to get (6 + 2b) + b = 42 6 + 3b = 42 3b = 36 b = 12 \a = 6 + 2b = 6 + 2(12) = 30
32.	Point must be strictly between 14 and 24. That is an interval of length 10. Answer: 10/PR = 10/30 = 1/3.
34.	From the givens, 2x – y = 12.5 Ù 3y – x = 12.5. Solve this system of linear equations using your favorite method from Algebra I (substitution, linear combinations, or whatever you like) to get x = 10, y = 7.5.
36.	x^2 – 27x = 90 x^2 – 27x – 90 = 0 (x + 3)(x – 30) = 0 x = –3 or x = 30
	Note: Problems 26, 34, and 36 provide review of Algebra I material. The following skills from Algebra I will be required throughout the year in Geometry and will not be retaught in class: § Solving a linear equation in which one variable is unknown (x or y, or any other variable that may be used) § Solving a system of two linear equations (i.e., finding the values of x and y that satisfy both equations) § Factoring a trinomial (e.g., #36) § Solving a quadratic equation (e.g., #36) by factoring when possible § Using the quadratic formula when factoring is awkward or not possible § Translating a verbal description of quantity relationships into equations (e.g., #26)
	If you are shaky or unclear about any of these skills, you need to visit the Math Lab and/or STAySmart Center to patch up the deficiencies.