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Trapezoids Practice

Problems 1 - 5 refer to the image below

Trapezoid A B C D, The midsegment is drawn.

Practice Problem #1

ABCD is an isosceles trapezoid. Segment AB is one base of trapezoid ABDC. What is the other base?
Answer: CD

Practice Problem #2

ABCD is an isosceles trapezoid. One of the base angles of ABDC is angle C. What is the other base angle?
Answer: Angle D

Practice Problem #3

ABCD is an isosceles trapezoid. Angle ___ and angle C are consecutive angles.
Answer: Angle A

Practice Problem #4

ABCD is an isosceles trapezoid. Angles D and ___ are supplementary.
Answer: Angle B

Practice Problem #5

ABCD is an isosceles trapezoid. What line represents the midsegment of ABDC?
Answer: The line going through the middle

Practice Problem #6

Find the missing angle measures.

Trapazoid A B C D has parallel bases A B and C D. Angle D is a right angle and Angle B is 132 degrees. These 2 angles are diagonal from each other

Remember, the consecutive angles in a trapezoid are supplementary.

Which angle is consecutive to ∠D? ∠___

Answer: ∠A

What about ∠B? ∠___

Answer: ∠C

Ok, let's solve for A first. Since A and D form a consecutive angle pair, they are supplementary. So,

∠A + ∠D = ___°

Answer: 180°

Substitute in the measure of ∠D.

∠A + ___° = 180°

Answer: 90°

Isolate the unknown value to solve.

∠A = ___°

Answer: 90°

Great! Now, let's solve for C. Since B and C form a consecutive angle pair, they are supplementary. So, ∠B + ∠C = 180°

Substitute in the measure of ∠B.

___° + ∠C = 180°

Answer: 132°

Isolate the unknown value to solve.

∠C = ___°

Answer: 48°

Practice Problem #7

Find the missing angle measures.

Trapazoid A B C D has parallel bases A B and C D. Angle D is a right angle and angle C = 112 degrees

Remember, the consecutive angles in a trapezoid are supplementary.

Which angle is consecutive to ∠D?

Answer: ∠A

Which angle is consecutive to ∠C?

Answer: ∠B

Ok, let's solve for A first. Since A and D form a consecutive angle pair, they are supplementary. So,

∠A + ∠D = ___°

Answer: 180°

Substitute in the measure of ∠D.

∠A + ___° = 180°

Answer: 90°

Isolate the unknown value to solve.

∠A = ___°

Answer: 90°

Great! Now, let's solve for B. Since B and C form a consecutive angle pair, they are supplemntary. So:

∠B + ∠C = 180°

Substitute in the measure of C.

∠B + ___° = 180°

Answer: 112°

Isolate the unknown value to solve.

∠B = ___°

Answer: 68°

Practice Problem #8

Find the length of segment RT.

A trapazoid has bases with length 9 and 12. The midsegment is labeled R T

Ok, so this is a midsegment problem. Remember,

midsegment = half the sum of the bases

Start by entering your known values.

R T = (9 + blank) over 2

Answer: 12

Simplify the numerator.

R T = blank over 2

Answer: 21

Simplify to solve. Put your answer in decimal format.

RT = ___

Answer: 10.5

Practice Problem #9

Find the length of segment PQ.

Trapazoid N P Q O has base N O with length 20. The midsegment R T has length 16. Base P Q is unknown and is labeled x

Even though you are not solving for the midsegment, you can still use the relationship between the midsegment and the bases to find the missing length.

R T = (P Q + N O) over 2

Start by entering your known values.

blank = (x + blank) over 2

Answer: 16, 20

Multiply both sides by 2 to eliminate the fraction.

___ = ___

Answer: 32, x + 20

Isolate the x to solve.

___ = x

Answer: 12