Grade 9 Mathematics Quiz: Congruent Segments and Angle Bisectors

Identify the congruent line segments in the given figure.

• AB and CD

• AC and BD

• AB and EF

• BC and DE

In the triangle ABC, if AB = AC, then prove that the line segments are congruent.

• The line segments are congruent because the triangle is equilateral.

• The line segments are congruent because the triangle is scalene.

• The line segments are congruent because the triangle is right-angled.

• The line segments are congruent because of the properties of an isosceles triangle.

Construct the angle bisector of angle XYZ.

• Use a compass to draw arcs from points X and Z, then draw a line through the vertex Y where the arcs intersect.

• Draw a line through the vertex Y without using any tools

• Use a protractor to measure the angle and then draw a line through the vertex Y

• Connect points X and Z with a straight line

Using angle bisectors, prove that the two angles formed are congruent.

• By using the Pythagorean theorem

• By using the Law of Sines

• By using the angle bisector theorem.

• By using the Law of Cosines

Find the measure of angle PQR using the angle bisector of angle PQS.

• Measure of angle PQR is equal to the measure of angle PQS

• Measure of angle PQR is greater than the measure of angle PQS

• Measure of angle PQR is unrelated to the measure of angle PQS

• Measure of angle PQR is half of the measure of angle PQS

Prove that the angles formed by the angle bisector are congruent.

• Angle bisector creates a right angle

• Angle bisector divides the angle into two unequal angles

• Angle bisector has no effect on the angle

• Angle bisector divides the angle into two congruent angles

Identify the congruent line segments in the given figure.

• AC and BD

• BC and DE

• AB and CD

• AB and EF

In the triangle DEF, if DE = DF, then prove that the line segments are congruent.

• Congruent by speculation

• Congruent by assumption

• Congruent by definition

• Congruent by coincidence

Construct the angle bisector of angle LMN.

• Use a compass to draw arcs from points L and N, then draw a line through point M where the arcs intersect.

• Draw two lines from points L and N and connect the endpoints to form the angle bisector

• Use a protractor to measure the angle and then draw a line through the midpoint of the angle

• Use a ruler to draw a line from point M to the midpoint of segment LN

Using angle bisectors, prove that the two angles formed are congruent.

• The two angles formed are congruent because of the Law of Cosines.

• The two angles formed are congruent because of the Law of Sines.

• The two angles formed are congruent because of the Pythagorean theorem.

• The two angles formed are congruent because of the angle bisector theorem.