Exam: 03.07 Module Three Review and Practice Exam Geometry

Kari drew two parallel lines PQ and RS intersected by a transversal KL, as shown below: Two parallel lines PQ and RS are drawn with KL as a transversal intersecting PQ at point M and RS at point N. Angle QMN is shown congruent to angle LNS. Which theorem could Kari use to show the measure of angle QML is supplementary to the measure of angle SNK?

Same-Side Interior Angles Theorem

In triangle ABC shown below, side AB is 6 and side AC is 4: Triangle ABC with segment joining point D on segment AB and point E on segment AC. 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.

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. Triangle ABC with medians CE, AF, and BD. Median AF is extended to point H. A segment joins points B and H and another segment joins points H and C. Which conclusion can be made based on the given conditions?

Segment GD is parallel to segment HC.

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

Angle PTR and angle PTS are supplementary angles.

The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent: Parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML. Extend segment JM beyond point M and draw point P, by Construction. An arrow is drawn from this statement to angle MLK is congruent to angle PML, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle PML is congruent to angle KJM, numbered blank 1. An arrow is drawn from this statement to angle MLK is congruent to angle KJM, Transitive Property of Equality. Extend segment JK beyond point J and draw point Q. An arrow is drawn from this statement to angle JML is congruent to angle QJM, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle QJM is congruent to angle LKJ, numbered blank 2. An arrow is drawn from this statement to angle JML is congruent to angle LKJ, Transitive Property of Equality. Two arrows are drawn from this previous statement and the statement angle MLK is congruent to angle KJM, Transitive Property of Equality to opposite angles of parallelogram JKLM are congruent. Which reasons can be used to fill in the numbered blank spaces?

Corresponding Angles Theorem 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 47°. Triangle ABC with segment DE. Angle ADE measures 47 degrees. The following flowchart with missing statements and reasons proves that the measure of angle ECB is 43°: Statement, Measure of angle ADE is 47 degrees, Reason, Given, and Statement, Measure of angle DAE is 90 degrees, Reason, Definition of right angle, leading to Statement 3 and Reason 2, which further leads to Statement, Measure of angle ECB is 43 degrees, Reason, Substitution Property. Statement, Segment DE joins the midpoints of segment AB and AC, Reason, Given, leading to Statement, Segment DE is parallel to segment BC, Reason, Midsegment theorem, which leads to Angle ECB is congruent to angle AED, Reason 1, which further leads to Statement, Measure of angle ECB is 43 degrees, Reason, Substitution Property. Which statement and reason can be used to fill in the numbered blank spaces?

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

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I took this test three times without help.

The figure below shows a rectangle ABCD having diagonals AC and DB: A rectangle ABCD is shown with diagonals AC and BD. 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) Which statement below completes Zinnia's proof?

Triangle ADC and BCD are congruent (by SAS postulate)

Look at the figure shown below: RQ is a segment on which a perpendicular bisector PS is drawn. S is the midpoint of RQ. 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.

The figure below shows a parallelogram ABCD. Side AB is parallel to side DC and side AD is parallel to side BC: A quadrilateral ABCD is shown with the two pairs of opposite sides AD and BC and AB and DC marked parallel . The diagonal are labeled BD and AC 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