Geometry Practice Test: Properties of Quadrilaterals
- Quadrilaterals
- 10 questions
- 13 minutes
These questions use the angle, side and diagonal properties of special quadrilaterals. Tip: a square is also a rectangle and a rhombus, so the most specific name is the one with every property that fits.
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Question 1
In parallelogram ABCD, m∠A = (3x + 15)° and m∠B = (2x + 5)°.
What is the measure of the larger angle of the parallelogram?
Correct answer: A
Consecutive angles of a parallelogram are supplementary: 5x + 20 = 180, so x = 32. Then m∠A = 111° and m∠B = 69°.
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Question 2
The diagonals of parallelogram ABCD intersect at E. AE = 2y + 3 and EC = 4y − 7.
What is the length of diagonal AC?
Correct answer: D
The diagonals of a parallelogram bisect each other, so 2y + 3 = 4y − 7 and y = 5. Each half is 13, and the whole diagonal is 26.
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Question 3
In rectangle ABCD, AC = 5x − 9 and BD = 3x + 11.
What is the length of BD?
Correct answer: C
The diagonals of a rectangle are congruent: 5x − 9 = 3x + 11 gives x = 10, so BD = 41. The value 20.5 would be half a diagonal.
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Question 4
Which property is true for every rhombus but not for every rectangle?
Correct answer: B
The diagonals of a rhombus always cross at right angles; the diagonals of a non-square rectangle do not. Congruent diagonals and right angles belong to rectangles, and parallel opposite sides belong to both.
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Question 5
Which given information is NOT enough to prove that a quadrilateral is a parallelogram?
Correct answer: C
An isosceles trapezoid has one pair of parallel sides and the other pair congruent, but it is not a parallelogram. The other three statements are standard tests for a parallelogram.
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Question 6
In an isosceles trapezoid, one of the angles at the longer base measures 64°.
What is the measure of each angle at the shorter base?
Correct answer: D
Angles on the same leg lie between parallel bases, so they are supplementary: 180° − 64° = 116°. Both angles at the shorter base are equal, because the trapezoid is isosceles.
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Question 7
A trapezoid has bases of 11 cm and 25 cm.
What is the length of its midsegment?
Correct answer: C
The midsegment of a trapezoid is the average of the bases: (11 + 25)/2 = 18 cm. The value 14 cm is the difference of the bases.
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Question 8
In kite ABCD, AB = AD and CB = CD. m∠A = 80° and m∠C = 50°.
What is m∠B?
Correct answer: A
In a kite, the angles between the pairs of unequal sides (∠B and ∠D) are congruent. They share 360° − 80° − 50° = 230°, so each is 115°.
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Question 9
The diagonals of a rhombus are 10 cm and 24 cm long.
What is the length of one side of the rhombus?
Correct answer: B
The diagonals bisect each other at right angles, forming right triangles with legs 5 cm and 12 cm. The side is 25 + 144 = 13 cm. Using the full diagonals as legs gives 26 cm.
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Question 10
The diagonals of a quadrilateral are congruent, perpendicular and bisect each other. What is the most specific name for the quadrilateral?
Correct answer: D
Bisecting diagonals make it a parallelogram, congruent diagonals make it a rectangle, and perpendicular diagonals make it a rhombus. A figure that is both is a square.
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