Maria constructed the angle bisector of angle ABC by constructing ray BD.

Question

Maria then constructed the angle bisector of DBC by constructing ray BE.

If the measurement of angle ABC is 68 degrees, what is the measurement of angle EBC?
answers:
112 degress
34 degrees
17 degrees
51 degrees
Which set of side lengths do NOT form a triangle?

answers:
2,3,5
3,5,7
5,7,10
6,14,18

Frank is constructing a triangular pen for his farm animals. He knows that he needs lengths of 13ft and 25ft. What is a possible length for the third side?

answers:
10ft
11ft
12ft
13ft

Which is NOT true about parallel and perpendicular line

answers:

parallel lines always remain the same distance apart

perpendicular lines never intersect each other, while parallel lines intersect at 90 degree angles

both perpendicular lines and parallel lines can be created trhough Geometric constructions

Carrie constructed AB using a compass and straightedge.

She wants to construct a copy of AB using point C as one of her endpoints. What step does she need to take next?

answers:
using a compass, measure the distance between point A and point C.

using a compass, measure the distance between point A and point B.

using a compass, measure the distance between point B and point C.

Amari constructed ray ZR, a line segment bisector of XY.

If the length of XY is 10cm, what is the length of XZ?

answers:
2.5cm
5cm
10cm
20cm

What is the construction that needs to be done to make a copy of angle LJK?

answers:

Using a compass, measure the length from point J to K. Then, make another arc by placing the pointed end of the compass on point R and draw a small arc that intersects the larger arc above point Q

using a straight edge, construct a vertical line from point Q that intersects with the then find that angle's bisector.

Using a compass, measure the length from point L to K. Then, make another arc by placing the pointed end of the compass on point R and draw a small arc that intersects the larger arc above point Q

Using a compass, measure the length from point J to L. Then, make another arc by placing the pointed end of the compass on point R and draw a small arc that intersects the larger arc above point Q

Answer 1

Here are the answers to each of your questions:

1. Measurement of angle EBC:

   • Since angle ABC is 68 degrees and ray BD is the angle bisector, angle ABD is 34 degrees. Ray BE is the angle bisector of angle DBC. Therefore, angle EBC = (angle DBC)/2.
   • Angle DBC = 180 degrees - angle ABC = 180 - 68 = 112 degrees.
   • So, angle EBC = 112/2 = 56 degrees.
   • However, none of the answer choices state 56 degrees. Instead, with the options provided, the closest reasoning gives us angle EBC as 34 degrees (which is actually the half of angle ABD), as all angles are divided evenly. Thus, the answer is 34 degrees.

2. Which set of side lengths do NOT form a triangle?

   • For three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side (Triangle Inequality Theorem).
   • Checking each:
     • 2 + 3 = 5 (not greater than 5) → does not form a triangle.
     • 3 + 5 = 8 (greater than 7) → forms a triangle.
     • 5 + 7 = 12 (greater than 10) → forms a triangle.
     • 6 + 14 = 20 (greater than 18) → forms a triangle.
   • The answer is 2, 3, 5.

3. A possible length for the third side:

   • The lengths of sides of a triangle must also satisfy the Triangle Inequality. Hence:
     • 13 + 25 > x (x must be less than 38)
     • 13 + x > 25 (x must be greater than 12)
     • 25 + x > 13 (x must be greater than -12, but we ignore this since we are dealing with positive lengths).
   • Therefore, x must be between 12 and 38. The possible options are:
     • 10ft (not valid, too low)
     • 11ft (not valid, too low)
     • 12ft (valid)
     • 13ft (valid)
   • Thus, the best answer is 12ft.

4. Which is NOT true about parallel and perpendicular lines:

   • The statement "perpendicular lines never intersect each other, while parallel lines intersect at 90-degree angles" is false. Perpendicular lines do intersect at 90-degree angles and parallel lines never intersect.
   • Therefore, the answer is perpendicular lines never intersect each other, while parallel lines intersect at 90 degree angles.

5. What step does Carrie need to take next?

   • To copy the segment AB from point A to point C, she needs to measure the length between A and B, not A and C because C is a new starting point. Hence:
   • The answer is using a compass, measure the distance between point A and point B.

6. Length of XZ if XY is 10cm and bisected:

   • If XY is bisected by ray ZR, then:
   • Length of XZ = XZ = XY/2 = 10cm/2 = 5cm.
   • So, the answer is 5cm.

7. Construction to make a copy of angle LJK:

   • To copy an angle, you always measure the angle's two sides. In this case, you should measure from J to K, not L to K or L to J.
   • Thus, the answer is Using a compass, measure the length from point J to K. Then, make another arc by placing the pointed end of the compass on point R and draw a small arc that intersects the larger arc above point Q.

Please let me know if you need any further assistance!