ACT 1 Geo: Use properties of quadrilaterals

Welcome to your ACT 1 Geo: Use properties of quadrilaterals

$Q1:$ Find the value of $x$ in the parallelogram shown below?

$10$

$8$

$4$

$0$

$Q_{2}:$ Find the area of parallelogram $PQRS$ shown below?

$60\sqrt{3}$

$12\sqrt{3}$

$5\sqrt{3}$

$\sqrt{3}$

$Q_{3}:$ What is the area of rhombus $ABCD$ below?

$12$

$16$

$20$

$24$

$Q_{4}:$ In $PQRS$ below, $PT= x+2 y$, $ST=8x-y$, $PR = 32 $, $TQ = 26 $, $m\angle 1 =6a$, $\angle 2=10a$, $m\angle 3=a^{2}-7$ and $m\angle PRS = 4a$. What is the value of $x $?

$8$

$6$

$4$

$2$

$Q_{5}:$ In $PQRS$ below, $PT= x+2 y$, $ST=8x-y$, $PR = 32 $, $TQ = 26 $, $m\angle 1 =6a$, $\angle 2=10a$, $m\angle 3=a^{2}-7$ and $m\angle PRS = 4a$. What is the value of $y$?

$8$

$6$

$4$

$2$

$Q_{6}:$ In $PQRS$ below, $PT= x+2 y$, $ST=8x-y$, $PR = 32 $, $TQ = 26 $, $m\angle 1 =6a$, $\angle 2=10a$, $m\angle 3=a^{2}-7$ and $m\angle PRS = 4a$. What is the measure of $\angle PQR $?

$110$

$111$

$112$

$113$

$Q_{7}:$ In the figure below, $PQRS$ is a parallelogram and $PTS$ is a right triangle. What is the area of the parallelogram $PQRS $?

$240$

$220$

$200$

$180$

$Q_{8}:$ Find the area of the quadrilateral shown below.

$30$

$60$

$64$

$64\sqrt{3} $

$Q_{9}:$ In square $ABCD$ below, the length of diagonal $AC$ is $5\sqrt{2}$. What is the area of the square?

$10$

$15$

$20$

$25$

$Q_{10}:$ What is the length of $AE $?

$7$

$7.5$

$8$

$8.5$

$Q_{11}:$ What is the area of trapezoid $PQRS$ below?

$20$

$24$

$26$

$32$

$Q_{12}:$ In the figure below, $\overline{EO}$ is the midsegment of trapezoid $TRAP$ and $\overline{RP}$ intersect $\overline{EO} at point $Z$ . If $RA = 15$ and $EO = 18 $, what is the length of $\overline{EZ }$?

$10.5$

$11.5$

$12.5$

$13.5$

$Q_{13}:$ A rectangle has a length that is $6$ meters more than twice its width. What is the perimeter of the rectangle if the area of the rectangle is $1620$ square meters?

$166$

$170$

$174$

$178$

$Q_{14}:$ The slopes of the sides of quadrilateral $ABCD$ are shown in the table below. Which statement describes the relationships between the sides of the quadrilateral?

$\overline{AD}$ is parallel to $\overline{BC}$, but $\overline{AB}$ is not parallel to $\overline{CD}$

$\overline{AB}$ is parallel to $\overline{CD}$, but $\overline{AD}$ is not parallel to $\overline{BC}$

$\overline{AB}$ is parallel to $\overline{CD}$, and $\overline{AD}$ is parallel to $\overline{BC}$

$\overline{AD}$ is not parallel to $\overline{BC}$, and $\overline{AB}$ is not parallel to $\overline{CD}$

$Q_{15}:$ If a quadrilateral is a square, then it has four congruent side. Which statement must also be true?

If a quadrilateral has four congruent sides, then it is a square.

If a quadrilateral does not have four congruent sides, then it is not a square.

If a quadrilateral is not a square, then it does not have four congruent sides.

If a quadrilateral does not have four congruent sides, then it is a square.

$Q_{16}:$ A figure $ABCD$ has an angle $A$ that measures $120$ degrees and angle $B$, which measures $60$ degrees. Angle $C$ is congruent to angle $A$ and angle $D$ is congruent angle $B$, and side length $AB$ is equal to side length $BC$. What type of figure is $ABCD$?

Rectangle

Trapezoid

Square

Rhombus

$Q_{17}:$ A figure $ABCD$ has side lengths $AB = CD= 4$, $BC = 10$, $AD=15$, and a height of $3.12$. If $BC$ and $AD$ are parallel to one another, what type of figure is $ABCD$?

Rectangle

Trapezoid

Square

Rhombus

$Q_{18}:$ The area of a rectangular painting is $24.5 ft^{2} $. 2 If the painting is $3.5 ft$ tall, what is its width?

$6.5$

$7$

$7.5$

$8$

$Q_{19}:$ What is the area of the parallelogram shown below?

$15$

$36$

$60$

$72$

$Q_{20}:$ The area of the trapezoid shown below is $72 cm^{2} $. What is the length of side $x$?

$15$

$16$

$17$

$18$

$Q_{21}:$ In any quadrilateral, the sum of the measures of the four angles is

$90$

$180$

$270$

$360$

$Q_{22}:$ The length of each side of a rhombus

is the same

are perpendicular

are angle bisectors

is the different

$Q_{23}:$ .................... is a quadrilateral in which exactly one pair of opposite sides is parallel.

A trapezoid

A rhombus

A rectangle

A square

$Q_{24}:$ The length of a rectangle is $5$ more than the side of a square, and the width of the rectangle is $5$ less than the side of the square. If the area of the square is $45$, what is the area of the rectangle?

$20$

$25$

$50$

$70$

$Q_{25}:$ In rhombus $PQRS$, the ratio of $m\angle P$ to $m\angle Q$ is $1$ to $5$ and $PQ = 6$. What is the area of the rhombus?

$12$

$6$

$18$

$30$

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