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Parallelograms: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

In parallelogram $ABCD$ , the side lengths in centimeters are given by
$\begin{gathered} AB=4x-5,\\ CD=27. \end{gathered}$
What is $x$ ?

Answer choices for question 1 A $5.5$ B $32$ C $8$ D $6.75$
2

Consecutive angles of a parallelogram measure $(3x+8)^\circ$ and $(4x+25)^\circ$ . What is $x$ ?

Answer choices for question 2 A $21$ B $-17$ C $\frac{180}{7}$ D $\frac{213}{7}$
3

The diagonals of parallelogram $ABCD$ meet at $E$ . The lengths in centimeters satisfy
$\begin{gathered} AE=x+7,\\ EC=3x-5. \end{gathered}$
What is the full length $AC$ ?

Answer choices for question 3 A $6$ cm B $13$ cm C $12$ cm D $26$ cm
4

In parallelogram $ABCD$ , diagonal $AC$ crosses the parallel sides $BC$ and $AD$ . Which angle is congruent to $\angle BCA$ by alternate interior angles?

Answer choices for question 4 A $\angle BAC$ B $\angle DAC$ C $\angle ABC$ D $\angle BCD$
5

In parallelogram $ABCD$ , diagonal $AC$ gives two alternate interior-angle pairs, and $AC$ is the common included side. Which conclusion uses those facts directly?

Answer choices for question 5 A $\triangle ABC\cong\triangle CDA$ by ASA B $\triangle ABC\cong\triangle ACD$ by ASA C The triangles are congruent by AAA D The triangles are congruent because all parallelograms have a reflection axis
6

Diagonal $AC$ of parallelogram $ABCD$ splits angle $DAB$ into $26^\circ$ and $41^\circ$ parts. What is the measure of angle $ABC$ ?

Answer choices for question 6 A $67^\circ$ B $154^\circ$ C $113^\circ$ D $139^\circ$
7

Parallelogram $ABCD$ has diagonal intersection $O$ . Under the half-turn about $O$ , which segment is the image of side $AB$ ?

Answer choices for question 7 A $BC$ B $CD$ C $AD$ D $AC$
8

Which list can be the four angles of a parallelogram $ABCD$ , in boundary order?

Answer choices for question 8 A $85^\circ$ , $85^\circ$ , $95^\circ$ , $95^\circ$ B $85^\circ$ , $95^\circ$ , $95^\circ$ , $85^\circ$ C $85^\circ$ , $85^\circ$ , $85^\circ$ , $85^\circ$ D $85^\circ$ , $95^\circ$ , $85^\circ$ , $95^\circ$
9

In the proof that parallelogram diagonals bisect each other, triangles $ABE$ and $CDE$ have two alternate interior-angle pairs. Which previously proved fact supplies the included side?

Answer choices for question 9 A $AE=CE$ B $BE=DE$ C $AB=CD$ D $AC=BD$
10

The diagonals of parallelogram $ABCD$ meet at $E$ . If $AE$ is $5$ cm and $BE$ is $3$ cm, which pair gives the full diagonal lengths?

Answer choices for question 10 A $AC$ is $5$ cm; $BD$ is $3$ cm B $AC$ is $10$ cm; $BD$ is $6$ cm C Both are $8$ cm D $AC$ is $6$ cm; $BD$ is $10$ cm
11

The solid outline is a parallelogram. The dashed red outline is its reflection in the horizontal line shown. What does the displayed mismatch establish by itself?

Answer choices for question 11 A That horizontal line is not a reflection axis of this parallelogram B This parallelogram has no half-turn symmetry C Every oblique parallelogram lacks all reflections D The solid shape is not a parallelogram
12

A quadrilateral is given to be a parallelogram. Under the inclusive trapezoid definition used here, which statement is correct?

Answer choices for question 12 A It cannot be a trapezoid because two pairs are parallel B It is a trapezoid only if its diagonals are congruent C It is a trapezoid only if all four sides are congruent D It is also a trapezoid because at least one opposite-side pair is parallel

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