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 arcs with center a. using the same arc, 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, 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 a 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 \(A\) and \(D\), he needs to draw an arc with radius \(BC\) and center \(E\) to complete the angle - copying construction.

When an angle is bisected, the bisector divides the angle into two equal - measure angles. If a student bisects \(\angle ABC\), then the point \(S\) on the bisector is such that \(\angle ABS=\angle SBC\).

Step1: Use vertical - angle property

Vertical angles are equal. \(\angle AEB\) and \(\angle DEC\) are vertical angles, so \(m\angle AEB=m\angle DEC = 50^{\circ}\). Also, \(\angle BEC\) and \(\angle AED\) are vertical angles.

Step2: Find \(x\)

We know that \(\angle AEB\) and \((x + 15)^{\circ}\) are vertical angles. So \(x+15 = 50\), then \(x=50 - 15=35\).

Step3: Find \(y\)

\(\angle AED\) and \((y + 30)^{\circ}\) are vertical angles. Since \(\angle AED=180 - 50=130^{\circ}\) (linear - pair with \(\angle AEB\)), then \(y + 30=130\), so \(y=100\).

Step4: Check each statement

• \(x = 35\), so statement A is true.
• \(y = 100\), so statement B is true.
• \(m\angle DEC = 50^{\circ}\), so statement C is true.
• \(m\angle BEC=180 - 50 = 130^{\circ}\), so statement D is false.
• \(m\angle AED = 130^{\circ}\), so statement E is true.

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.