Question

geometry chapter 1 review

1. jorge wrote the following steps for copying an angle. is jorge missing any step? if yes, please identify the missing step.

step 1
draw a segment.
draw an angle such as ∠a, as shown. then draw a segment. label point d on the segment.
step 2
draw arcs.
draw an arc with center a. using the same radius, draw an arc with center d.
step 3
draw a ray.
draw (overrightarrow{df}). ∠d has the same measure as ∠a.
a. jorges construction is not missing any step.
b. jorges construction is missing a step. the missing step is: draw an arc. label b, c, and e. draw an arc with a radius smaller than bc and center e. label the intersection f.
c. jorges construction is missing a step. the missing step is: draw an arc. label b, c, and e. draw an arc with a radius larger than bc and center e. label the intersection f.
d. jorges construction is missing a step. the missing step is: draw an arc. label b, c, and e. draw an arc with a radius bc and center e. label the intersection f.

1. a student used a compass and a straightedge to bisect ∠abc in this figure.

which statement best describes point s?
a. point s is located such that (mangle abc=mangle sbc).
b. point s is located such that (mangle pbq = mangle pqs).
c. point s is located such that (mangle apb=mangle apq).
d. point s is located such that (mangle abs=mangle sbc).

1. in the figure below lines ac and bd intersect at point e. select all the statements that are true.

a. (x = 35)
b. (y = 100)
c. (mangle dec=50^{circ})
d. (mangle bec = 100^{circ})
e. (mangle aed=130^{circ})

Explanation:

12.

When copying an angle using a compass and straight - edge, after drawing arcs from the vertex of the given angle and from the starting point of the new ray, we need to draw an arc with the radius equal to the distance between the intersection points of the arcs on the given angle, centered at the intersection point of the arc on the new ray. In Jorge's steps, after drawing arcs from the vertex of ∠A and from point D, he needs to draw an arc with radius equal to the distance between the intersection points of the arcs on ∠A (say BC) centered at the intersection point of the arc on ray DF (point E). The correct step is to draw an arc. Label B, C, and E. Draw an arc with a radius BC and center E. Label the intersection F.

When bisecting an angle ∠ABC using a compass and straight - edge, the ray that divides the angle into two equal - measure angles is called the angle bisector. If a ray BS bisects ∠ABC, then m∠ABS=m∠SBC.

Vertical angles are equal. ∠AED and ∠BEC are vertical angles, and ∠DEC and ∠AEB are vertical angles. ∠AEB = 50° (vertical angles with the given 50° angle), so ∠DEC=50°. ∠AED + ∠AEB=180° (linear pair), so ∠AED = 130°. Also, ∠BEC = 130°. For the equations, if we assume vertical - angle relationships, we have no information to solve for x and y from the given figure.

Answer:

D. Jorge's construction is missing a step. The missing step is: Draw an arc. Label B, C, and E. Draw an arc with a radius BC and center E. Label the intersection F.

13.