EOC Review: Quadrilaterals

Given parallelogram 𝐾𝐿𝑀𝑁, what is the value of 𝑠?

• 5

• 20

• 40

• 70

Answer explanation

Consecutive angles of a parallelogram are supplementary (=180)

Tags

CCSS.HSG.CO.C.11

Given parallelogram 𝐴𝐵𝐶𝐷 below, find the value of 𝑥.

Mathematical Equivalence

ON

Answer explanation

Opposite angles of a parallelogram are congruent.

Tags

CCSS.HSG.CO.C.11

Given parallelogram 𝐺𝐻𝐽𝐾, find the values of 𝑎 and 𝑏.

• 𝑎=2 and 𝑏=24

• 𝑎=2 and 𝑏=42

• 𝑎=7 and 𝑏=24

• 𝑎=7 and 𝑏=42

Answer explanation

In a parallelogram, opposite sides are congruent & opposite angles are congruent.

Tags

CCSS.HSG.CO.C.11

In parallelogram 𝐴𝐵𝐶𝐷, 𝐴𝐶=𝐷𝐵, 𝑚∠𝐴𝐵𝐶=2𝑥𝑦, and 𝑚∠𝐵𝐶𝐷=9𝑥+9. Find the value of 𝑦.

Mathematical Equivalence

ON

Answer explanation

When you draw a diagram, you realize that if the diagonals are congruent, the parallelogram must be a RECTANGLE, so each angle must equal 90 degrees.

Tags

CCSS.HSG.CO.C.11

Given rectangle 𝑊𝑋𝑌𝑍 below with 𝑊𝑉=18, find 𝑋𝑍. Enter your answer in the box.

Mathematical Equivalence

ON

Answer explanation

In a rectangle, diagonals are congruent and bisected!

Tags

CCSS.HSG.CO.C.11

Given rectangle 𝑄𝑅𝑆𝑇 with 𝑚∠𝑃𝑇𝑆=34° and 𝑄𝑆=10, select All the true statements.

• 𝑚∠𝑄𝑇𝑅=56°

• 𝑚∠𝑄𝑅𝑇=34°

• 𝑚∠𝑆𝑅𝑇=34°

• 𝑄𝑃=5

• 𝑅𝑇=10

Answer explanation

In a rectangle, diagonals are congruent and bisected. All angles are right angles (=90).

Tags

CCSS.HSG.CO.C.11

Given rectangle 𝐷𝐸𝐹𝐺 below, select all the true statements.

• 𝑥+𝑦=12

• 𝐷𝐻 = 14

• 𝑚∠𝐺𝐷𝐻=30°

• 𝑚∠𝐹𝐸𝐻=60°

• 𝑚∠𝐹𝐻𝐸=60°

Answer explanation

In a rectangle, since diagonals are congruent and bisected, you can set each segment part equal and solve for x.

Use vertical angles and the isosceles triangle to solve for the missing angle measure.

Tags

CCSS.HSG.CO.C.11

The diagonals of square 𝐴𝐵𝐶𝐷 intersect at point 𝐸. If 𝐵𝐸 = 2𝑥 + 1 and 𝐴𝐶 = 3(6𝑥 − 4), what is the length of 𝐵𝐷?

Mathematical Equivalence

ON

Tags

CCSS.HSG.CO.C.11

Paulina bought a camping tent with a parallelogram-shaped flysheet as drawn below. If 𝑚∠𝐴𝐶𝐷=73°, what is the value of 𝑥?

Mathematical Equivalence

ON

Answer explanation

Consecutive angles of a parallelogram are supplementary.

Tags

CCSS.HSG.CO.C.11

One angle of an isosceles trapezoid has a measure of 53°. What are the measures of the other three angles of the trapezoid?

• 37°, 127°, 127°

• 53°, 127°, 127°

• 37°, 135°, 135°

• 53°, 82°, 82°

Answer explanation

In an isosceles trapezoid, OPPOSITE ANGLES are SUPPLEMENTARY; CONSECUTIVE ANGLES are CONGRUENT.