WorksheetsGEOMETRY (S2) Pre-Assessment
Total questions: 55
Worksheet time: 38mins
Which of the following pairs of angles proves that two lines are parallel?
Linear pair
Alternate interior angles
Vertical angles
Complementary angles
If two lines are cut by a transversal and the corresponding angles are congruent, what can you conclude?
The lines are skew.
The lines are parallel.
The lines are perpendicular.
The lines form a triangle.
Which of the following is NOT a valid method to prove two lines parallel?
Corresponding angles are congruent.
Same-side interior angles are supplementary.
Alternate interior angles are congruent.
Adjacent angles are complementary.
What does the Converse of the Alternate Interior Angles Theorem state?
Parallel lines form alternate interior angles.
Alternate interior angles are always equal.
If alternate interior angles are congruent, then the lines are parallel.
If alternate exterior angles are congruent, then the lines are parallel.
How is the distance from a point to a line determined?
By measuring along the x-axis.
By finding the shortest perpendicular segment from the point to the line.
By using the slope of the line.
By measuring any segment connecting the point to the line.
A line is perpendicular to another line if:
The slopes are equal.
The slopes are negative reciprocals.
The angles they form are obtuse.
The slopes are identical.
If a line has a slope of , what is the slope of a line perpendicular to it?
-4/3
4/3
-3/4
¾
Which of the following relationships is true for perpendicular lines?
The lines intersect to form complementary angles.
The lines form acute angles only.
The lines intersect at 90°.
The lines have equal slopes.
Which of the following triangles always has at least two congruent sides?
Scalene
Isosceles
Acute
Right
What type of triangle has one angle measuring 90°?
Acute triangle
Scalene triangle
Obtuse triangle
Right triangle
A triangle with one angle greater than 90° is classified as:
Acute
Right
Obtuse
Scalene
The sum of the interior angles of a triangle is always:
90°
180°
If a triangle has angles measuring 40° and 60°, what is the measure of the third angle?
80°
90°
100°
110°
In a right triangle, what is the measure of the two acute angles?
Always equal
Always complementary
Always supplementary
Always congruent
What do you call the exterior angle of a triangle?
The sum of two remote interior angles
Equal to one interior angle
Complementary to an adjacent angle
Twice the adjacent interior angle
Two triangles are congruent if:
All corresponding sides are equal.
All corresponding angles are equal.
Both sides and angles match.
They have the same perimeter.
Which postulate cannot prove triangle congruence?
What does the Congruence Postulate state?
All triangles with equal sides are congruent.
Two triangles are congruent if they have the same shape and size.
Triangles with equal areas are congruent.
Triangles with equal perimeters are congruent.
What is an example of non-congruent triangles?
SSS
SSA
SAS
AAS
Which congruence postulate requires three pairs of corresponding sides to be congruent?
ASA
SSS
SAS
AAS
The SAS postulate states that two triangles are congruent if:
If two triangles are congruent by SSS, what must be true?
All angles are equal.
All corresponding sides are equal.
Both a and b.
Only the perimeters are equal.
In triangle congruence, the term “included angle” means:
The angle between two given sides.
Any angle in the triangle.
The largest angle in the triangle.
The smallest angle in the triangle.
Which congruence postulate requires two angles and a side to be congruent?
SSS
ASA
SAS
AAS
What is the difference between ASA and AAS postulates?
ASA requires a side to be included between the two angles.
AAS requires a side to be included between the angles.
ASA does not require an included side.
AAS requires all three sides to be equal.
Which statement is true about AAS congruence?
The side must be between the angles.
The angles must be adjacent.
The side does not need to be between the angles.
The side must be equal to all other sides.
If two triangles are congruent by ASA, what must be true?
Two angles and their included side are congruent.
All angles are congruent.
Two sides are congruent.
The perimeters are equal.
In an isosceles triangle, the angles opposite the congruent sides are called:
Base angles
Vertex angles
Adjacent angles
Right angles
What is true about an equilateral triangle?
All sides are equal.
All angles measure 60°.
Both a and b.
It always contains a right angle.
In an isosceles triangle, the non-congruent side is called the:
(a)
When a triangle is reflected across a line, what happens to its size and shape?
Both size and shape change.
Size changes, but shape remains.
Neither size nor shape changes.
Only the angles change.
What is the first step in proving triangles congruent using the coordinate plane?
Calculate the slope of all sides.
Use distance formula to find the lengths of the sides.
Find the midpoints of each side.
Translate the triangle to the origin.
Which formula is often used in coordinate proofs to find the length of a triangle’s side?
Slope formula
Distance formula
Midpoint formula
Pythagorean theorem
In a coordinate proof, how can you prove a triangle is isosceles?
Show all angles are equal.
Prove two sides have the same length.
Show all sides are equal.
Show one angle is a right angle.
What is required for a triangle to be congruent using the coordinate plane?
A perpendicular bisector divides a segment into:
Two congruent parts at a 90° angle.
Two congruent parts at any angle.
Two parts, one of which is larger.
Unequal parts at a right angle.
The point of concurrency of the perpendicular bisectors of a triangle is called the:
Incenter
Circumcenter
Centroid
Orthocenter
In a triangle, the circumcenter is equidistant from:
The sides
The vertices
The midpoints of the sides
The altitudes
Which of the following statements about angle bisectors is true?
A median of a triangle connects a vertex to:
The opposite side at a right angle.
The midpoint of the opposite side.
The longest side of the triangle.
The shortest side of the triangle.
The point where the medians of a triangle intersect is called the:
Circumcenter
Incenter
Centroid
Orthocenter
What is true about the centroid of a triangle?
It divides each median into a 1:1 ratio.
It divides each median into a 2:1 ratio.
It is always outside the triangle.
It is equidistant from all three vertices.
An altitude of a triangle is:
A segment connecting a vertex to the opposite side at a right angle.
A segment connecting the midpoints of two sides.
A segment that divides an angle into two congruent angles.
In a triangle, the longest side is always opposite the:
Smallest angle
Largest angle
Right angle
Median
The sum of the lengths of any two sides of a triangle must be:
Greater than the length of the third side.
Equal to the length of the third side.
Less than the length of the third side.
Twice the length of the third side.
If one side of a triangle is longer than another, then the angle opposite the longer side is:
Smaller than the angle opposite the shorter side.
Larger than the angle opposite the shorter side.
Equal to the angle opposite the shorter side.
A right angle.
Which of the following is a valid inequality in a triangle with side lengths a, b, and c?
a + b < c
a + b - c
a + b > c
a - b < c
What is the first step in writing an indirect proof?
Prove the statement directly.
Assume the opposite of what you want to prove.
Draw a diagram of the situation.
State the conclusion immediately.
An indirect proof is also called:
A formal proof
A direct proof
A proof by contradiction
A geometric proof
In an indirect proof, what do you show to disprove the assumption?
A logical contradiction
A congruent triangle
A parallel line
A right angle
Which of the following is an example of an indirect reasoning strategy?
Showing all possibilities are true
Showing one possibility is false
Showing all possibilities except one are false
Proving something without any assumptions
Which of the following sets of side lengths can form a triangle?
3, 5, 8
4, 7, 12
6, 9, 15
5, 5, 9
What must be true about the sum of the lengths of two sides of a triangle?
It must equal the length of the third side.
It must be greater than the length of the third side.
It must be less than the length of the third side.
It must form a right angle.
Which set of inequalities represents the triangle inequality theorem for a triangle with sides a, b, and c?
a + b > c, a + c > b, b + c > a
a + b < c, a + c < b, b + c < a
a + b - c, a + c = b, b + c - a
a + b > c, a - c > b, b - c > a
The Triangle Inequality Theorem can be used to:
Determine whether a given set of side lengths forms a triangle.
Prove that all angles in a triangle are congruent.
Find the perimeter of a triangle.
Solve for unknown side lengths in a triangle.
