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WorksheetsGeometry Quiz
Total questions: 106
Worksheet time: 2hrs 58mins
The measure of two angles in a triangle are 60° and 85°. What is the measure of the third angle?
40°
80°
45°
60°
Corresponding parts of congruent triangles are _____________.
Corresponding
Similar
Parallel
Congruent
Which statement is correct?
If two pairs of corresponding angles and an included side are congruent, the triangles are congruent.
If any two pairs of sides and an angle are congruent, the triangles are congruent.
If any pairs of sides and angles are congruent, the triangles are congruent.
All triangles are congruent because they all have 180°.
The measure of 2 angle of a triangle are 60° and 75°. What is the measure of the third angle?
40°
80°
45°
60°
Which of the statements below provides sufficient information to guarantee that two triangles are congruent?
The triangles have three pairs of congruent corresponding angles.
The triangles have two pairs of congruent corresponding sides and one pair of congruent corresponding angles.
Identify the missing congruent parts in the diagram:
Find the value of the variable that makes the triangles congruent.
Are these triangles congruent? Explain.
Identify the type of triangle in the given figure.
Right Triangle
Equilateral Triangle
Isosceles Triangle
Scalene Triangle
In the figure below, find the missing angles measure.
50∞
55∞
65∞
The diagram shows an isosceles triangle. What is the measure of angle A?
40∞
50∞
60∞
65∞
If one angle of a parallelogram is 60°, what is the measure of its consecutive angle?
120°
90°
60°
180°
In a parallelogram, the diagonals always...
Bisect each other
Are equal in length
Are perpendicular to each other
Divide the parallelogram into four equal triangles
Which set of side lengths cannot form a triangle according to the Triangle Inequality Theorem?
6 cm, 4 cm, 8 cm
5 cm, 7 cm, 12 cm
6 cm, 9 cm, 14 cm
9 cm, 5 cm, 5 cm
An equilateral triangle has three angles of (a) degrees each.
The sum of the interior angles of any triangle is (a) degrees.
The opposite angles in a parallelogram are always (a) .
Consecutive angles of a parallelogram are always (a) angles.
A parallelogram has one side of 10 cm and another side of 6 cm. can the perimeter be 30cm? Explain.
What is the measure of the exterior angle of an equilateral triangle?
Which of the following statements is always true for a parallelogram?
All angles measure 90°
Opposite sides are both equal and parallel
The diagonals intersect at right angles
Only two sides are parallel
If a four-sided figure has two pairs of opposite sides that are both equal in length and parallel, what type of shape is it?
Trapezoid
Rectangle
Parallelogram
Kite
A parallelogram has one angle measuring 60°. What are the measures of the other three angles?
60°,120°,60°
60°,120°,120°
90°,90°,90°
30°,150°,30°
Which statement about the diagonals of a parallelogram is correct?
They are always of equal length
They bisect each other at their midpoint
They always form right angles
They do not intersect
Which is the formula for calculating the slope of a line passing through two points (x1,y1) (x2,y2)?
If two lines have the same slope then, the lines are:
Perpendicular
Parallel
Intersecting at 90°
Coinciding
Which is the slope of a line that passes through the points (4,2) and (9,6)?
1/5
1/2
1/3
5/4
Match each quadrilateral to one of its characteristics. Write the number next to each quadrilateral's corresponding property. Match each property to only on quadrilateral.
Line l is ‖ to line M if the slope of line l is 7/5 the slope for line M must be __________.
The slope of a horizontal line is always ________.
A student asserts that while squares are rectangles, Rectangles can not be squares. Discuss why this statement holds true based on the properties of these quadrilaterals.
Draw a line parallel to the line below then complete the statement below. The slope of the line is ___________________.
If cos(30°) = , what is sin(60°)?
1
1/2
√3/2
√2/2
Which of the following equations correctly represents the sine ratio for angle A in a right triangle?
sin A = adjacent/hypotenuse
sin A = opposite/hypotenuse
sin A = hypotenuse/opposite
sin A = adjacent/opposite
What is the definition of the tangent ratio in a right triangle?
Adjacent / Hypotenuse
Opposite / Hypotenuse
Opposite / Adjacent
Hypotenuse / Opposite
If, which of the following is true?
The opposite side is equal to the hypotenuse.
The opposite side is equal to the adjacent side.
The adjacent side is equal to the hypotenuse.
The opposite side is twice the adjacent side.
Which equation correctly represents the tangent ratio for angle A in a right triangle?
tan A = opposite/adjacent
tan A = adjacent/opposite
tan A = hypotenuse/opposite
tan A = hypotenuse/adjacent
The cosine of an angle in a right triangle is the ratio of the (a) side to the hypotenuse.
The tangent of an angle in a right triangle is the ratio of the (a) side to the adjacent side.
Match each trigonometric value to its correct angle measure:
A ladder leans against a wall forming a 65° angle with the ground. If the ladder is 12 feet long, how high does it reach on the wall? Show your calculations using the cosine ratio.
A ramp rises to a height of 2.5 meters over a horizontal distance of 6 meters. Find the angle of elevation using the tangent ratio. Show your calculations.
The measure of 2 angles of a triangle are 60° and 85°. What is the measure of the third angle?
40°
80°
45°
60°
Complete the statement below. Corresponding parts of congruent triangles are ________________.
Corresponding
Similar
Parallel
Congruent
Which of these statements is correct?
If any 2 pairs of sides and angle are congruent then the triangles are congruent.
If any 2 pairs of corresponding angles and an included side are congruent then the triangles are congruent.
If any pairs of sides and angles are congruent then the triangles are congruent.
All triangles are congruent because they all have 180°.
Study the diagram below and complete each statement.
Determine whether the given triangles are congruent.
Find the value of the variable that results in congruent triangles.
Identify the type of triangle in the given figure.
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
Right Triangle
In the figure below, find the missing angles measure.
50°
55°
65°
75°
Which statement about an equilateral triangle is correct?
Only two sides are equal
All angles measure 60°
The sum of all angles is 270°
It has one right angle
On an equilateral triangle, If one side is 7 cm, what is the perimeter?
14 cm
21 cm
28 cm
35 cm
The diagram shows an isosceles triangle. What is the measure of angle A?
40°
50°
60°
80°
The remote angles to an exterior angle of a triangle are _______________________
the angles adjacent to the exterior angle
the angles that share the same vertex with the exterior angle
the angles that are on the same line as the exterior angle
the interior angles that do not share the same vertex with but sum up to the exterior.
Complete each statement below. An isosceles triangle has exactly (a) equal sides.
An equilateral triangle has three angles of (a) degrees each.
The sum of the interior angles of any triangle is (a) degrees.
In an isosceles triangle, the two equal sides are called __________, and the third side is called the __________.
legs
base
Which set of side lengths can form a triangle according to the Triangle Inequality Theorem?
6 cm, 4 cm, 8 cm
5 cm, 7 cm, 12 cm
6 cm, 8 cm, 14 cm
9 cm, 5 cm, 3 cm
What does the Triangle Inequality Theorem state?
The sum of two sides of a triangle must be greater than the third side.
The sum of any two sides must be equal to the third side.
The longest side must always be twice the shortest side.
The difference between two sides must always be greater than the third side.
Which of the following statements is true?
A triangle can have sides measuring 2 cm, 3 cm, and 7 cm.
A triangle must have all three angles equal to 90°.
The sum of any two sides of a triangle must be greater than the third side.
The smallest angle in a triangle is always opposite the longest side.
Which of the following is always true about a parallelogram?
Opposite sides are equal and parallel
All angles are right angles
Diagonals are perpendicular
All sides are equal
If one angle of a parallelogram is 120°, what is the measure of its consecutive angle?
120°
90°
60°
180°
In a parallelogram, the diagonals always...
Bisect each other
Are equal in length
Are perpendicular to each other
Divide the parallelogram into four equal triangles
Fill in the blank: If a triangle has sides of lengths 8 cm and 15 cm, the possible values for the third side must be between _____________________ cm and _____________________ cm.
7
23
Fill in the blank: In any triangle, the longest side is always opposite the (a) angle.
The opposite angles in a parallelogram are always (a) .
Consecutive angles of a parallelogram are always (a) angles.
A hiking trail forms a triangle between three mountains: A, B, and C. The distances between the mountains are: Mountain A to Mountain B: 12 km Mountain B to Mountain C: 9 km What is the possible range for the distance from Mountain A to Mountain C?
Between 3 km and 21 km
Between 4 km and 25 km
Between 1 km and 15 km
Between 4 km and 20 km
Which of the following is always true for a parallelogram?
All angles are right angles
Opposite sides are equal and parallel
Diagonals are perpendicular
Only one pair of sides is parallel
If a quadrilateral has opposite sides that are both parallel and equal in length, what type of shape is it?
Trapezoid
Rhombus
Parallelogram
Kite
Which condition is NOT sufficient to prove a quadrilateral is a parallelogram?
Opposite sides are equal
Opposite angles are equal
One pair of opposite sides is both equal and parallel
The diagonals are perpendicular
A parallelogram has angles measuring 70° and 110°. What is the measure of the other two angles?
70° and 110°
90° and 90°
80° and 100°
60° and 120°
Which of the following quadrilaterals is always a parallelogram?
A rhombus
A trapezium
A kite
A triangle
Which of the following is true about the diagonals of a parallelogram?
They are always equal in length
They bisect each other
They are perpendicular
They never intersect
Fill in the Blank: A quadrilateral is a parallelogram if one pair of opposite sides is both _________________ and _________________ .
equal
parallel
Fill in the Blank: If the diagonals of a parallelogram are equal, then the parallelogram is a (a) .
Match the quadrilateral to one of its properties write the number next to each quadrilateral to its corresponding property: Quadrilateral Property 1 Rhombus Opposite sides are equal and all angles are 90° 2 Rectangle All sides are equal 3 Parallelogram All sides and angles are equal 4 Square Opposite sides are equal and parallel
A quadrilateral has one pair of opposite sides equal and parallel. However, its diagonals are not equal. Can we conclude that this shape is a parallelogram? Justify your answer.
A student claims that a parallelogram with equal diagonals is necessarily a square. Do you agree? Explain why or why not.
Which of the following is always true about a rectangle?
All four sides are equal
All four angles are right angles
Diagonals are perpendicular
It has only one pair of parallel sides
Which of the following is a property of a rhombus but NOT necessarily a rectangle?
Diagonals bisect each other
Opposite sides are parallel
All sides are equal in length
Opposite angles are equal
Which of the following conditions is true for all parallelograms?
All angles are 90 degrees
Opposite sides are parallel and equal
All four sides are equal
Diagonals are equal in length
Which of the following statements about a rectangle is FALSE?
Opposite sides are parallel
The diagonals bisect each other
The diagonals are perpendicular
It has four right angles
What is the formula for calculating the slope of a line passing through two points (x1,y1) (x2,y2)?
If the slopes of two lines are equal, the lines are:
Perpendicular
Parallel
Intersecting at 90°
Coinciding
What is the slope of a line that passes through the points (3,2) and (7,6)?
1/5
1/2
1/3
1/1
Two consecutive line segments m and l of a parallelogram have slopes 1/2 and -1/2. what are the slopes of the other two line segments of the parallelogram?
1/3 and -1/5
1/2 and 1/-2
1/2 and 1/2
-1/2 and -1/2
Fill in the blank: The slope of a horizontal line is always (a) .
Two lines are parallel if they have the same (a) .
A (a) is a parallelogram with four right angles and equal diagonals.
A rhombus has diagonals that are ______________ and _______________ each other.
perpendicular
bisect
Proof-Based Question: A student claims that all squares are rhombuses, but not all rhombuses are squares. Explain why this statement is true using properties of quadrilaterals.
What is the coordinate of the fourth vertex of the parallelogram?
What is the slope of a line perpendicular to a line with a slope of 3?
3
-3
1/3
-1/3
If two lines are perpendicular, their slopes are:
Equal
Opposite
Negative reciprocals
The same as their y-intercepts
Which equation represents a line perpendicular to y=2x+5?
y= -1/2x+3
y= 2x−1
y= 1/2x+4
y= −2x+7
Which formula is used to find the distance between two points (x1,y1) and (x2,y2) in a coordinate plane?
What is the distance between the points A(3,4) and B(7,1)?
5 units
7 units
6 units
8 units
If two segments have the same length in a coordinate proof, what can be concluded?
They are perpendicular
They are parallel
They are congruent
They bisect each other
Given the points P(2,3), and Q(6,7), what is the length of segment PQ?
4√2
5
6
3√2
Triangle ABC has vertices at A(1,2), B(4,6), and C(7,2). Prove whether △ABC is isosceles.
Yes, because AB=BC
Yes, because AC = BC.
No, because all sides are different
Yes, because AB = AC.
Which of the following statements is true about perpendicular lines?
They have the same slope
Their slopes add up to zero
Their slopes are negative reciprocals
They never intersect
Determine if the lines with equations y=−1/4x+2 and y=4x−3 are perpendicular.
Yes
No
Cannot be determined
Only if they have the same y-intercept
A quadrilateral has vertices A(1,2), B(4,6), C(7,2), and D(4,-2). Prove that the diagonals of the quadrilateral are perpendicular. By finding the slopes of AC and BD.
Prove that the triangle formed by points A(−1,3), B(3,7), and C(7,3) is a right triangle. By comparing the slopes of all three segments.
