Chapter 1 Review Problems

Problem Set A

1) Describe in words the set of points that are 5 units away from a circle with radius 5 units.

2) The measure of the supplement of an angle is 150° more than half the measure of the angle. Find the measure of the angle.

Supplementary angles will add to 180°.

3) Find the following:

a. $\overrightarrow{SG} \cup \overrightarrow{SE} =$ ___________

b. $\overrightarrow{NI} \cap \overrightarrow{SN} =$ ___________

c. $\overline{GI} \cup \overline{GE} =$ ___________

d. $\overline{ES} \cap \overline{IN} =$ ___________

e. Name all the angles that are less than 180° with vertex at point G.

4) Given: $\overline{NM}$ is the ⊥ bisector of $\overline{IE}$ , ∠MSA = (3x + 3y)° , SE = 6y − 5 , AE = 2x

(a bisector splits an object into 2 equal parts)

Determine the length of $\overline{AE}$ .

5) Find the measure of the (smaller) angle formed by the hands of a clock at 12:45.

6) Given: $\overline{GS}$ ⊥ $\overline{VA}$ , ∠ESG = (8x + 5)° , ∠VSE = (x² + 20)°

Prove: $\overline{ES}$ bisects ∠VSG

Give a reason for your initial equation, do the algebraic work, and give a reason for your concluding statement.

7) Given: $\overline{AE} \perp \overline{EC} , \overline{BE} \perp \overline{ED}$

∠AEB = (10x + 2y)° ,

∠BEC = (12x − 4y)° ,

∠CED = (8x − 6y)°

Find the measure of ∠BEC.

8) Given: Diagram as shown

Find: m∠BSE + m∠ASR

9) Draw and describe a picture to represent the set of all points that are equidistant from two parallel lines.

10) Rotate quadrilateral BART 90° counter-clockwise about point R.

11)

Given:

$\overlines{DB}$ bisects $\overline{AC}$
AB = 4y − 7 , BC = 2y + 5

Find the length of $\overline{AC}$ .

12) State all symmetries in each figure.

Problem Set B

13)

Given:

$\overline{BE} \perp \overline{AL}$ , ∠ABE = (18x − 2y)° ,
∠EBD = (-6y)° , ∠DBL = (9x)°

Find: m∠EBD

14) Determine the smaller angle made by the hands of a clock at 4:10.

15) On a graph, Point A is at (0,4). Point A is then rotated 90° clockwise about the origin to point A’. What are the coordinates of point A’ ?

16) PQRS is a rectangle.

a) Find the coordinates of Point P.

b) Find the area of the rectangle.

17)

a. Point P is reflected over the y-axis to point A. Find the coordinates of A.

b. Point P is reflected over the origin to point B. Find the coordinates of B.

c. If C is the midpoint of $\overline{PA}$ , find the coordinates of C.

18) Use a ruler to translate ∆TOM by vector v.

19) Use a ruler, compass, and protractor to rotate figure TRAP clockwise 270º around point S.

20) Rotate quadrilateral BART counter-clockwise 120º around point S. Label the image appropriately.

21) a. How many angles are in the diagram?

b. If the measures of of ∠1, ∠2, and ∠3 are in the ratio of 4 : 5 : 6, what is the measure of the largest angle?

Problem Set C

22) Use a ruler, compass, and protractor to reflect ∆WIN over line l and then rotate image ∆W’I’N’ 90° counter-clockwise about point P.

23) Translate ∆DOG by vector v and then reflect the image over line s. Label the image appropriately.

24) In problems #22 and #23, are either pair of transformations commutative? That is, if you switched the order of the operations would the result be the same?

25) At 9:00 the hands of a clock form an angle of 90°. To the nearest second, at what time will the hands of the clock next form a 90° angle?

See the answers