Level 2 · Intermediate ← Back to lesson

Rectangles, Rhombi, and Squares: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

Rectangle $ABCD$ has whole diagonals with these lengths, in centimeters.
$\begin{gathered}AC=6x+1\\BD=4x+15\end{gathered}$
Find $x$ .

Answer choices for question 1 A $4$ B $8$ C $7$ D $14$
2

In rhombus $PQRS$ , angle $QPR$ measures $27^\circ$ . What is the measure of the whole angle at $Q$ ?

Answer choices for question 2 A $126^\circ$ B $54^\circ$ C $153^\circ$ D $63^\circ$
3

A parallelogram has perpendicular diagonals of lengths $18$ cm and $30$ cm. Which is the strongest guaranteed classification?

Answer choices for question 3 A A square B A rectangle that is not a square C A parallelogram that cannot be a rhombus D A rhombus that is not a square
4

In parallelogram $ABCD$ , diagonal $AC$ bisects angle $DAB$ . Which triangle fact completes a proof that it is a rhombus?

Answer choices for question 4 A Triangle $ABC$ must have three right angles B Triangle $ABC$ has congruent angles at $A$ and $C$ C Triangle $ABC$ has no congruent sides D Triangle $ABC$ has congruent angles at $A$ and $B$ because they are consecutive parallelogram angles
5

A convex quadrilateral has diagonals meeting at $O$ . Its diagonals bisect each other and the whole diagonals are congruent. What is guaranteed?

Answer choices for question 5 A A rectangle, with square still possible B A square, with no other case possible C A rhombus that cannot be a rectangle D Only an arbitrary quadrilateral
6

In the rectangle proof, triangles $DAB$ and $CBA$ have $AD=BC$ , common side $AB$ , and right included angles. Which congruence test proves them congruent?

Answer choices for question 6 A SSS using diagonals already known congruent B SSA C SAS D AAA
7

Rhombus $ABCD$ has diagonals meeting at $O$ . The lengths of $AO$ and $BO$ are $7$ cm and $24$ cm, respectively. Find $AB$ .

Answer choices for question 7 A $31$ cm B $25$ cm C $17$ cm D $50$ cm
8

Convex quadrilateral $ABCD$ is built from four perpendicular rays at $O$ . The lengths $AO$ , $OC$ , $BO$ , and $OD$ are $4$ , $2$ , $3$ , and $3$ units, respectively. Which statement is true?

Answer choices for question 8 A Its diagonals bisect each other B It is a square because both diagonals have length 6 C It is a rhombus because its diagonals are perpendicular D Its diagonals are congruent, but it is not a rectangle
9

The diagonals of rhombus $ABCD$ meet at $O$ . Which comparison proves that angles $AOB$ and $AOD$ are congruent without assuming perpendicularity?

Answer choices for question 9 A The triangles are congruent by SAS using right angles at O B The angles are vertical angles C The diagonals have equal lengths in every rhombus D $\triangle AOB\cong\triangle AOD$ by SSS
10

A parallelogram has one right angle and two congruent adjacent sides. What is the strongest guaranteed classification?

Answer choices for question 10 A A square B A rectangle that is not a rhombus C A rhombus that is not a rectangle D A parallelogram that might have no right angles
11

Rectangle $JKLM$ has diagonals meeting at $O$ . The half-diagonal lengths, in centimeters, are given below.
$\begin{gathered}JO=3x-2\\KO=x+6\end{gathered}$
Find $x$ .

Answer choices for question 11 A $2$ B $6$ C $4$ D $8$
12

Which evidence guarantees a square for a convex quadrilateral?

Answer choices for question 12 A Its diagonals are congruent and perpendicular, with no other evidence B Its diagonals bisect each other and are both congruent and perpendicular C Its diagonals bisect each other, with no other evidence D It has exactly two congruent opposite sides, with no other evidence

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