Geometry Exam Review

Naomi draws a portion a figure as shown. She wants to construct a line segment through R that makes the same angle with line QR as line PQ. Which figure shows the next step to construct a congruent angle at R? Answer: https://docs.google.com/document/d/12sCjoR9THVVMxooqFY-iAoyGuWBYcNgLTJjCbWWlCiQ/edit?usp=sharing

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Brenda observes that the keyboard and the screen of open laptop lie on two different planes. In how many lines do the planes containing the keyboard and the screen intersect?

1

Part of a line that has two endpoints

Line Segment

Which of the following is a defined term?

Angle

Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS. Which could be the measures of angle POS and angle POQ?

m<POS=20 degrees, m<POQ=40 degrees

An architect plans to draw a rectangular patio with segment LM representing one side of the rectangle. He wants to construct a line passing through Q and parallel to side LM. He uses a straightedge and compass to complete some steps of the construction. Which of these is likely to be his next step in constructing the parallel line?

Without changing the width of the compass, place the compass at Q and draw an arc similar to the one drawn.

Stella is using her compass and straightedge to complete a construction of a polygon inscribed in a circle. Which polygon is she in the process of constructing?

A regular hexagon

Michael is using a drawing program to complete a construction. Which construction is he completing? Image: https://docs.google.com/document/d/12sCjoR9THVVMxooqFY-iAoyGuWBYcNgLTJjCbWWlCiQ/edit?usp=sharing

A square inscribed in a circle

A line is an undefined term because it

is a term that does not have a formal definition.

The following is an incomplete flowchart proving that the opposite angle of parallelogram JKLM are congruent. Which reasons can be used to fill in the numbered blank spaces?

1. Alternate

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 degrees 2. Triangle Sum Theorem 3. Corresponding angle are congruent

When constructing an inscribed equilateral triangle, how many arcs will be draw on the circle?

6

Ben uses a compass and a straightedge to bisect angle PQR. Which statement best explains why Ben uses the same width to draw arcs from A and b which intersect at S?

<AQS≅BQS when AS = BS and AQ = BQ.

Which statement best compares a line and a point?

A point has no dimension and a line has one dimension.

Which statement is true about a line and a point?

A point is a location and a line has many points located on it.

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 angleCDB 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

Maria drew two parallel lines KL and MN intersected by transversal PQ. Which theorem could Maria use to show the measure of angle KRQ is equal to the measure of angle PSN?

Alternate Interior Angles Theorem

What construction does the image below demonstrate? (Equilateral triangle inscribed in a circle) Image: https://docs.google.com/document/d/12sCjoR9THVVMxooqFY-iAoyGuWBYcNgLTJjCbWWlCiQ/edit?usp=sharing

An equilateral triangle inscribed in a circle.

PQ and RS are two lines that intersect at point T. Which statement is used to prove that angle PTR is always equal to angle STQ?

Angle PTR and angle PTS are supplementary angles.

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, AB = DC (opposite sides of rectangle are congruent)

A series of points that extend in two directions without end

Line

Which of the following is the final step in bisecting a line segment?

Mark the intersection of the arcs, and draw a line through those two points.

Lines that lie in the same plane and do not intersect

Parallel lines

Two lines that intersect at angles

Perpendicular Lines

In triangle ABC , side AB is 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.

Which conclusion can be made based on the given conditions?

Segment GD is half the length of segment HC.

Which of these is a correct step in constructing an angle bisector?

Use a compass to draw two equal arcs from the intersection points of pervious arc and the legs.

A flat surface that extends infinitely and has no thickness.

Plane

Which of the following terms is a set of all points in a plane that are a given distance from a point?

Circle

Jaira is completing a construction of regular hexagon inscribed in a circle as shown below. What should be the next step in her construction? Image: https://docs.google.com/document/d/12sCjoR9THVVMxooqFY-iAoyGuWBYcNgLTJjCbWWlCiQ/edit?usp=sharing

Construct another point E by placing her compass at point D.

Which of these is a step in constructing and inscribed regular hexagon using technology?

Create circle b with radius AB.

Rafeal wrote the statement shown in the chart below: Statement 1: If the point lies outside a line, then exactly one plane contains both the line and the point. Statement 2: If two points lie in a plane, then the line joining them lies in that plane.

Statement 1 is a theorem because it can be proved, and Statement 2 is a postulate because it is a true fact.

The figure below shows a partially completed set of steps to construct a rhombus PQRS: Student 1:Fix the compass at M and adjust its width to point L. Without changing the width of the compass, move the compass to N and draw a small arc on the big arc. Label the point of intersection of the two arcs as T. Draw a line segment from P that passes through T. Adjust the width of the compass to QR and draw an arc from point P to intersect line PT at S. Student 2: Fix the compass at M and draw an arc that intersects side QP at point T. Without changing the width of the compass, move the compass to R and draw an arc. Adjust the width of the compass to QR and draw an arc from point P. Draw a line segment from R that passes through T and intersects the second arc at S. Student 3: Fix the compass at L and adjust its width to point M. Without changing the width of the compass, move the compass to R and draw an arc which intersects QR at point T. Draw a line segment from R that passes through T and intersects the arc at S. Student 4: Fix the compass at L and adjust its width to point P. Without changing the width of the compass, move the compass to R and draw an arc which intersects QR at point T. Draw a line segment from R that passes through T and intersects the arc at S.

Student 1

Ken drew a pair of intersecting rays and marked the angle between them. Which statement best compares the pair of intersecting rays with the angle?

The rays extend infinitely, and the angle is made by the rays which have a common endpoint.

Which step should be used to prove that point A is equidistant from points C and B?

Triangle ABD is congruent to triangle ACD.