Geometry B U2 L3 Proving That a Quadrilateral Is a Parallelogram Answers

1. Complete this statement: A polygon with all sides the same length is said to be ______.
Answer - B. Equilateral

2. A road sign is in the shape of a regular heptagon. What is the measure of each angle on the sign? Round to the nearest tenth.
Answer - A. 128.6°

3. In the figure, the horizontal lines are parallel and AB=BC=CD. Find the measure of JM. The diagram is not drawn to scale.
Answer - B. 21

4. Find the sum of the measures of the interior angles of the figure.
Answer - B. 720

5. Find the value of x. The diagram is not drawn to scale.
Answer - C. x = 99

6. The sum of the measures of two exterior angles of a triangle is 264°. What is the measure of the third exterior angle?
Answer - B. 96

7. How many sides does a regular polygon have if each exterior angle measures 72°?
Answer - C. 5

8. What are the missing reasons in the proof?
Answers - 3. definition of parallelogram
4. alternate interior angles theroem
5. reflexive property of congruence
6. ASA

9.Based on the information in the diagram, determine whether the figure is a parallelogram. If so, select the answer with the correct justification.
Answer - D. Yes, both pairs of opposite sides are congruent.

10. Complete the two-column proof.
Answers - 2. SV // TU
3. SV // TU
7. Corresponding part of congruent triangle
8. Definition of parallelogram.

100% Hope this helps! Btw, this is only the first half of the quiz. The second half is different for everyone.

But just in case some people have the same "part 2 quiz" questions that I did, here they are...

1. Find the values of the variables x,y, and z in the parallelogram. The diagram is not drawn to scale. (diagram shows a tilted square with 33 in top left corner, 109 in top right, z in bottom left, and x and y in bottom right.)

Answer - x=33, y=38, z=109
Explanation -
x=33 (alternate angles)
33+109+y=180
142+y=180
y=180-142
y=38
z=109

2. In parallelogram DEFG, DH = x + 1, HF = 3y, GH = 3x − 4, and HE = 5y + 1. Find the values of x and y. The diagram is not drawn to scale.
Answer -
DH = HF     
x + 1 = 3y         
y = (x + 1) ⁄ 3        

GH = HE
 3x – 4 = 5y + 1
  y = (3x – 5) ⁄ 5
             
 y = y
 (x + 1) ⁄ 3 = (3x – 5) ⁄ 5
5x + 5 = 9x – 15
4x = 20
 x = 5

y = (x + 1) ⁄ 3        
y = (5 + 1) ⁄ 3       
y = 2 

3. If ON = 8x − 8, LM = 7x + 4, NM = x − 5, and OL = 3y − 6, find the values of x and y for which LMNO must be a parallelogram. The diagram is not drawn to scale.
Answer -
ON = LM
8x-8 = 7x+4
x = 12

OL = NM
3y-6 = x-5
3y-6 = 12-5
3y = 13
y = 13/3

No name is 100 percent right for part 1 of quiz 👍

no name is right on test one i had the same answers as them for test two so

On the 2nd part of the test on question 2, Instead of setting the values equal to each other we would set them equal to 180 right?

I correct myself

You're not that guy pal, you're not that guy.

@no name, bro thank you so much

I am wrong

Thanks No name

To find the answers to these questions, you will need to apply various concepts and properties of geometry. Here's how you can approach each question:

1. To identify a polygon with all sides the same length, you need to recall the definition of an equilateral polygon. An equilateral polygon has all sides of equal length, so the answer is B. Equilateral.

2. A regular heptagon has seven sides of equal length, and the sum of its interior angles is given by the formula (n-2) * 180, where n is the number of sides. In this case, n equals 7. So, you can calculate the measure of each interior angle by dividing the sum by 7. The closest rounded value to the nearest tenth is 128.6°, so the answer is A.

3. In the figure with parallel horizontal lines and equal lengths of AB, BC, and CD, you need to determine the measure of angle JM. Since AB is parallel to CD, the alternate interior angles are congruent. Angle JMC is congruent to angle BMA because of the alternate interior angles theorem. And since AB = BC and AB is parallel to BC, triangle BCA is an isosceles triangle, so angle ABJ is congruent to angle CBJ. Thus, angles ABJ and JMC are congruent since they are corresponding angles of parallel lines. Since angle ABJ is 21, angle JMC is also 21, so the answer is B.

4. The sum of the measures of the interior angles of any polygon can be found using the formula (n-2) * 180, where n is the number of sides. In this case, the figure is a quadrilateral, so it has four sides (n = 4). Plugging the value into the formula, you get (4-2) * 180 = 360°. So, the sum of the measures of the interior angles is 360°, and the answer is B.

5. To find the value of x in the diagram, you can use the fact that opposite angles in a parallelogram are congruent. The angles labeled 3x-18 and 6x-18 are opposite angles, so they must be congruent. Setting these angles equal to each other and solving for x gives you:
3x - 18 = 6x - 18
3x = 6x
-3x = -18
x = 6. So, the value of x is 6, and the answer is C.

6. The sum of the measures of the exterior angles of any polygon is always 360°. In a triangle, the sum of the measures of the three exterior angles is 360°. You are given the sum of two exterior angles, which is 264°. Subtracting 264° from 360° gives you the measure of the third exterior angle. So, the answer is B, 96°.

7. The exterior angle of a regular polygon is equal to 360° divided by the number of sides. In this case, you are given that the measure of each exterior angle is 72°. Setting up the equation, you get:
360° / x = 72°, where x represents the number of sides. Solving for x gives you:
360° = 72° * x
360° / 72° = x
5 = x. So, the regular polygon has 5 sides, and the answer is C.

For question 8 and beyond, it would be helpful to have the specific proof or diagram to provide further assistance.