3.09 Module 3 Practice Exam

The figure shows triangle ABC with medians AF, BD, and CE. Segment AF is extended to H in such a way that segment GH is congruent to segment AG. Which conclusion can be made based on the given conditions?

Segment GD is half the length of segment HC.

The figure shows triangle ABC with medians AF, BD, and CE. Segment AF is extended to H in such a way that segment GH is congruent to segment AG. Which conclusion can be made based on the given conditions?

Segment GD is parallel to segment HC.

PQ and RS are two lines that intersect at point T, as shown below: Which fact is used to prove that angle PTS is always equal to angle RTQ?

Sum of the measures of angles RTQ and QTS is 180°.

Look at the figure shown below: Which step should be used to prove that point A is equidistant from points C and B?

Triangle ABD is congruent to triangle ACD.

The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:

1. Alternate Interior Angles Theorem 2. Corresponding Angles Theorem

The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:

1. Corresponding Angles Theorem 2. Corresponding Angles Theorem

Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 68°. The following flowchart with missing statements and reasons proves that the measure of angle ECB is 22°: Which statement and reason can be used to fill in the numbered blank spaces?

1. Corresponding angles are congruent 2. Triangle Sum Theorem 3. Measure of angle AED is 22°

Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 47°. The following flowchart with missing statements and reasons proves that the measure of angle ECB is 43°: Which statement and reason can be used to fill in the numbered blank spaces?

1. Corresponding angles are congruent 2. Triangle Sum Theorem 3. Measure of angle AED is 43°.

Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 36°. The following flowchart with missing statements and reasons proves that the measure of angle ECB is 54°: Which statement and reason can be used to fill in the numbered blank spaces?

1. Measure of angle AED is 54° 2. Triangle Sum Theorem 3. Corresponding angle are congruent

The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent

1. ∠ PML ≅ ∠ KJM2. Corresponding Angles Theorem

The figure below shows a parallelogram ABCD. Side AB is parallel to side DC and side AD is parallel to side BC: A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal: For triangles ABD and CDB, alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines. Similarly, alternate interior angle ADB is equal to angle CBD because AD and BC are parallel lines. DB is equal to DB by reflexive property. Therefore, triangles ABD and CDB are congruent by _______________. Therefore, AB is congruent to DC and AD is congruent to BC by CPCTC. Which phrase best completes the student's proof?

ASA Postulate

Estelle drew two parallel lines PQ and RS intersected by a transversal KL, as shown below: Which theorem could Estelle use to show the measure of angle KMQ is equal to the measure of angle RNL?

Alternate Exterior Angles Theorem

Maria drew two parallel lines KL and MN intersected by a transversal PQ, as shown below: Which theorem could Maria use to show the measure of angle KRQ is equal to the measure of angle PSN?

Alternate Interior Angles Theorem

PQ and RS are two lines that intersect at point T, as shown below :Which statement is used to prove that angle PTR is always equal to angle STQ?

Angle PTR and angle PTS are supplementary angles.

The figure below shows a rectangle ABCD having diagonals AC and DB: Jimmy wrote the following proof to show that the diagonals of rectangle ABCD are congruent: Jimmy's proof: Statement 1: In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent) Statement 2: Angle ADC = Angle BCD (angles of a rectangle are 90°) Statement 3: Statement 4: Triangle ADC and BCD are congruent (by SAS postulate) Statement 5: AC = BD (by CPCTC) Which statement below completes Jimmy's proof?

DC=DC (reflexive property of equality)

PQ and RS are two lines that intersect at point T, as shown below: Which fact is used to prove that angle PTR is always equal to angle STQ?

If two angles are equal to the same measure, then the angles are congruent.

Look at the figure shown below: Which step should be used to prove that point P is equidistant from points R and Q?

If two sides and one included angle are equal in triangles PQS and PRS, then their third sides are equal.

The figure below shows a rectangle ABCD having diagonals AC and DB: Anastasia wrote the following proof to show that the diagonals of rectangle ABCD are congruent: Anastasia's proof: Statement 1: Statement 2: AB = DC (opposite sides of a rectangle are congruent) Statement 3: AC2 = DB2 (from statements 1 and 2) Statement 4: AC = DB (taking square root on both sides of AC2 = DB2) Which statement below completes Anastasia's proof?

In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent)

Look at the figure shown below: Which step should be used to prove that point A is equidistant from points C and B?

In triangles ABD and ACD, two sides and an included angle are equal.

The figure shows triangle ABC with medians AF, BD, and CE. Segment AF is extended to H in such a way that segment GH is congruent to segment AG. Which conclusion can be made based on the given conditions?

Segment EG is half the length of segment BH.

The figure shows triangle ABC with medians AF, BD, and CE. Segment AF is extended to H in such a way that segment GH is congruent to segment AG. Which conclusion can be made based on the given conditions?

Segment EG is parallel to segment BH.

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel: A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram: Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle BDC, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by _______________. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which phrase best completes the student's proof?

SAS Postulate

In triangle ABC shown below, side AB is 6 and side AC is 4: Which statement is needed to prove that segment DE is parallel to segment BC and half its length?

Segment AD is 3, and segment AE is 2.

In triangle ABC shown below, side AB is 8 and side AC is 4: Which statement is needed to prove that segment DE is half the length of segment BC?

Segment AD is 4, and segment AE is 2.

n triangle ABC shown below, side AB is 10 and side AC is 8: Which statement is needed to prove that segment DE is parallel to segment BC and half its length?

Segment AD is 5, and segment AE is 4.

The figure below shows a rectangle ABCD having diagonals AC and DB: Zinnia wrote the following proof to show that the diagonals of rectangle ABCD are congruent: Zinnia's proof: Statement 1: In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent) Statement 2: Angle ADC = Angle BCD (angles of a rectangle are 90°) Statement 3: DC = DC (reflexive property of equality) Statement 4: Statement 5: AC = BD (by CPCTC)

Triangle ADC and BCD are congruent (by SAS postulate)

Look at the figure shown below: Which step should be used to prove that point P is equidistant from points R and Q?

Using SAS postulate, prove that triangles PQS and PRS are congruent.

Chelsea drew two parallel lines KL and MN intersected by a transversal PQ, as shown below: Which theorem could Chelsea use to show the measure of angle KRP is equal to the measure of angle QRL?

Vertical Angles Theorem

The figure below shows a quadrilateral ABCD. Sides AB and DC are equal and parallel: A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram: Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle CDB, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and BCD are congruent by SAS postulate. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB _______________. Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

form a pair of alternate interior angles which are congruent

The figure below shows a parallelogram ABCD. Side AB is parallel to side DC and side AD is parallel to side BC: A student wrote the following sentences to prove that the two pairs of parallel opposite sides of parallelogram ABCD are congruent: For triangles ABD and CDB, alternate interior angles ABD and CDB are congruent because AB and DC are parallel lines. Alternate interior angles ADB and CBD are congruent because AD and BC are parallel lines. DB is congruent to DB by _______________. The triangles ABD and CDB are congruent by ASA postulate. As corresponding parts of congruent triangles are congruent, AB is congruent to DC and AD is congruent to BC by CPCTC. Which phrase best completes the student's proof?

reflexive property