Question 1(Multiple Choice Worth 1 points)
(01.05 MC)
What is the inverse of the following conditional statement?
"If the figure is a triangle, then the figure has three sides."
If the figure has three sides, then the figure is a triangle.
If the figure is a triangle, then the figure can have only three sides.
If the figure does not have three sides, then the figure is not a triangle.
If the figure is not a triangle, then the figure does not have three sides.
Question 2(Multiple Choice Worth 1 points)
(01.07 MC)
Line CT and line SM intersect at point A. What is the relationship between angle CAM and angle TAS?
Angle CAM and angle TAS are supplementary angles that sum to 180°.
Angle CAM and angle TAS are vertical angles that are congruent.
Angle CAM and angle TAS are supplementary angles that are congruent.
Angle CAM and angle TAS are vertical angles that sum to 180°.
Question 3(Multiple Choice Worth 1 points)
(01.02, 01.06 LC)
Mike constructed a quadrilateral POQS. He used a compass and straightedge to accurately construct line segment OS, as shown in the figure below:
An angle POQ is drawn. Two similar arcs intersect OP and OQ. Two more similar arcs intersect each other at a point S, and a dashed line is drawn from O to S, such that OS bisects angle POQ.
Which could be the measures of angle POS and angle POQ?
Measure of angle POS is 30 degrees, measure of angle POQ is 50 degrees.
Measure of angle POS is 30 degrees, measure of angle POQ is 65 degrees.
Measure of angle POS is 25 degrees, measure of angle POQ is 65 degrees.
Measure of angle POS is 25 degrees, measure of angle POQ is 50 degrees.
Question 4(Multiple Choice Worth 1 points)
(01.05 LC)
What is the converse of the following statement?
"If cows make milk, then chickens make eggs."
If chickens make eggs, then cows make milk.
If cows make milk, then chickens do not make eggs.
If cows do not make milk, then chickens do not make eggs.
If chickens do not make eggs, then cows do not make milk.
Question 5(Multiple Choice Worth 1 points)
(01.02 LC)
Ian is bisecting segment CD. First, Ian places the compass on point D, opens it to a width larger than half of the segment, and swings an arc on both sides of segment CD. Then, Ian keeps the compass the same width and places it on the other point C. What is the next step?
Swing arcs on both sides of segment CD to intersect the first two arcs created.
Swing an arc above line segment CD.
Swing an arc that intersects the opposite point D.
Swing an arc that intersects segment CD.
Question 6(Multiple Choice Worth 1 points)
(01.06 MC)
In the figure, lines m and n are parallel.
Two parallel lines are shown crossed by a transversal. The angles are labeled with number 1-8. The angles on line m where the line is crossed by the transversal are 1, 2, 4, and 3 in clockwise order from top left. The angles on line n where the line is crossed by the transversal are 5, 6, 8, and 7 in clockwise order from top left.
If m∠7 = 92°, what is m∠8?
8°
88°
92°
180°
Question 7(Multiple Choice Worth 1 points)
(01.05 MC)
Read the following statements:
Statement 1: If it is a square, then it has more than four sides.
Statement 2: If it has less than four sides, then it is a square.
Determine if the statements are true or false and if they have the same meaning.
Both statements are true and they have the same meaning.
Both statements are false and they have the same meaning.
Both statements are true and they do not have the same meaning.
Both statements are false and they do not have the same meaning.
Question 8(Multiple Choice Worth 1 points)
(01.06 MC)
Which statement justifies why ∠DBC measures 40°?
Given: angles ABD and DBC are complementary
Point B is on line AE between points A and E, point B is on line FD between points F and D, ray BC intersects with line AE at point B, line FD intersects with line AE at point B, the measure of angle ABD is 50 degrees, and it is given that angles ABD and DBC are complementary.
A linear pair is two adjacent, supplementary angles.
The sum of the measures of complementary angles is 90 degrees.
If two angles are vertical angles, then they are congruent.
The sum of the measures of supplementary angles is 180 degrees.
Question 9(Multiple Choice Worth 1 points)
(01.02 MC)
Nadia draws a portion of a figure, as shown. She wants to construct a line segment through R that makes the same angle with line segment QR as line segment PQ.
A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first but of the same measure and intersects QR. A compass with its ends at points S and T is shown.
Which figure shows the next step to construct a congruent angle at R?
A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first but of the same measure and intersects QR. A line segment RX is drawn that makes the same angle with QR as QP makes with QR. A straightedge is placed along the length of RX.
A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first arc but of the same measure and intersects QR. A compass is shown drawing a small arc across the big arc near R.
A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first arc but of the same measure and intersects QR. A small arc is drawn across the big arc near R. A straightedge is placed along the small arc.
A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first arc but of the same measure and intersects QR. A small arc is drawn across the big arc near R. A compass is placed at the point of intersection of the arcs, and the compass is shown making another arc below the intersecting arcs.
Question 10(Multiple Choice Worth 1 points)
(01.07 LC)
Find the measure of x.
Line PU has points R and S between points P and U, lines QR and ST are parallel, line QR intersects line PU at point R, line ST intersects line PU at point S, the measure of angle PRQ is 135 degrees, and the measure of angle UST is 15 open parenthesis x plus 2 close parenthesis degrees.
x = 8
x = 7
x = 9
x = 11
Question 11(Multiple Choice Worth 1 points)
(01.06 LC)
Which of the following explains the relationship between angles A and B?
Lines JK and JM intersect at point J, creating four angles identified as angle A, angle D, angle C, and angle A clockwise from the top right.
Adjacent angles
Corresponding angles
Complementary angles
Vertical angles
Question 12(Multiple Choice Worth 1 points)
(01.05 LC)
Give a counterexample to disprove the following statement.
"If the polygon is a quadrilateral, then the diagonals bisect each other."
Rectangle
Rhombus
Kite
Square
Question 13(Multiple Choice Worth 1 points)
(01.07 MC)
Which of the following correctly justifies statement 4 of the two-column proof?
Lines JK and LM are intersected by transversal JL; the intersection of JK and JL creates angles 2, 4, 3, and 1 clockwise beginning at the top right; the intersection of LM and JL creates angles 6, 8, 7 and 5 clockwise beginning at the top right.
Given: line JK is parallel to line LM
Prove: ∠2 ≅ ∠7
Statement Justification
1. line JK is parallel to line LM 1. Given
2. ∠6 ≅ ∠7 2.
3. ∠2 ≅ ∠6 3.
4. ∠2 ≅ ∠7 4.
Corresponding Angles Theorem
Transitive Property of Equality
Vertical Angles Theorem
Substitution Property of Equality
Question 14(Multiple Choice Worth 1 points)
(01.07 MC)
Examine the paragraph proof. Which theorem does it offer proof for?
Segments JK and HI are parallel, segment LO intersects segment JK at point N, segment LO intersects segment HI at point M, and points N and M are between points L and O on segment LO.
Prove: ∠JNM ≅ ∠NMI
According to the given information in the image, segment JK is parallel to segment HI while ∠JNM and ∠LNK are vertical angles. ∠JNM and ∠LNK are congruent by the Vertical Angles Theorem. Because ∠LNK and ∠NMI are corresponding angles, they are congruent according to the Corresponding Angles Theorem. Finally, ∠JNM is congruent to ∠NMI by the Transitive Property of Equality.
Alternate Interior Angles Theorem
Corresponding Angles Theorem
Vertical Angles Theorem
Same-Side Interior Angles Theorem
Question 15(Multiple Choice Worth 1 points)
(01.06 MC)
Ray BE bisects ∠ABC. If m∠ABE = (3x + 8)° and m∠CBE = (7x − 8)°, what is m∠CBE?
4°
9°
20°
40°
Question 1: If the figure does not have three sides, then the figure is not a triangle.
Question 2: Angle CAM and angle TAS are vertical angles that are congruent.
Question 3: Measure of angle POS is 25 degrees, measure of angle POQ is 65 degrees.
Question 4: If chickens make eggs, then cows make milk.
Question 5: Swing arcs on both sides of segment CD to intersect the first two arcs created.
Question 6: 88°
Question 7: Both statements are false and they do not have the same meaning.
Question 8: The sum of the measures of complementary angles is 90 degrees.
Question 9: A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first but of the same measure and intersects QR. A compass is shown drawing a small arc across the big arc near R.
Question 10: x = 11
Question 11: Vertical angles
Question 12: Kite
Question 13: Corresponding Angles Theorem
Question 14: Corresponding Angles Theorem
Question 15: 20°