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Geometry Foundations Review and Practice Test 1.09 FLVS (80%)
Terms in this set (15)
Ethan is using his compass and straightedge to complete a construction of a polygon inscribed in a circle. Which polygon is he in the process of constructing?
A circle with a diameter is drawn with two arc markings shown.
An equilateral triangle
Which of the following explains the relationship between angles A and D?
Lines JK and JM intersect at point J, creating four angles identified as angle B, angle D, angle C, and angle a clockwise from the top right.
Which of the following is part of a line that has two endpoints?
Which statement is true about a line and a point?
!!!N O T!!! A point and a line have length as a dimension to measure.
When constructing an equilateral triangle, what step comes after six arcs are created on the circle?
Connect every other intersection of an arc and the circle with a segment.
Beck 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?
m∠POS = 60°, m∠POQ = 120°
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: Segment JK is parallel to Segment LM
Prove: ∠2 ≅ ∠7
1. Segment JK is parallel to
Segment LM 1. Given
2. ∠6 ≅ ∠7 2.
3. ∠2 ≅ ∠6 3.
4. ∠2 ≅ ∠7 4.
!!!N O T!!! Corresponding Angles Theorem
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.
The sum of the measures of complementary angles is 90 degrees.
Examine the paragraph proof. Which theorem does it offer proof for?
lines WZ and XY intersect at point V
Prove: ∠XVZ ≅ ∠WVY.
We are given an image of segment WZ and segment XY, which intersect at point V. m∠XVZ + m∠ZVY = 180° by the Definition of Supplementary Angles. m∠ZVY + m∠WVY = 180° by the Definition of Supplementary Angles. Since the sum of m∠XVZ + m∠ZVY = m∠ZVY + m∠WVY by the Transitive Property of Equality, m∠ZVY can be subtracted from both sides of the equation because of the Subtraction Property of Equality. Therefore, m∠XVZ = m∠WVY and ∠XVZ ≅ ∠WVY by the definition of congruent angles.
Vertical Angles Theorem
Alice is designing a bookshelf. The segment LQ represents the base of the bookshelf. Alice wants to construct a line to represent a rack passing through R and parallel to side LQ. She uses a straightedge and compass to complete some steps of the construction, as shown below:
A line segment LQ is drawn. A transversal that intersects LQ at N is drawn. T is a point at the other end of the transversal. A compass is set at R, and an arc is drawn that cuts NT at T.
Which of these is likely to be her next step in constructing the rack parallel to LQ?
Place the compass at S, and adjust its width to point P.
Nadia draws a portion of a figure, as shown. She wants to construct a line segment through R that makes the same angle with as segment QR as PQ
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.
The figure below shows a partially-completed set of steps to construct parallelogram PQRS:
Two sides of a parallelogram PQRS are drawn. PQ makes an acute angle with the horizontal side QR. QR extends to the left, and an arc is drawn that cuts this extended line at L and the side QP at M. An arc of the same measure and the same orientation as arc LM is drawn from point R to cut QR at N. Another small arc intersects this arc at T. The position of T is such that a line segment drawn through RT makes the same angle with QR as angle LQM.
The next step is to construct side RS of the parallelogram so that side RS is congruent to side PQ. The chart below shows the steps each of the four students took to draw side RS of the parallelogram:
Student 1: 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. Draw a line segment from R that passes through T and intersects the arc at S.
Student 2:Fix the compass at Q, and draw an arc that intersects side QP. Without changing the width of the compass, move the compass to R and draw an arc. Draw a line segment from R that passes through T and intersects the second arc at S.
Student 3: Fix the compass at Q, and adjust its width to point P. Without changing the width of the compass, move the compass to R and draw an arc. 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. Draw a line segment from R that passes through T and intersects the arc at S.
Which student used the correct steps to construct parallelogram PQRS?
!!!N O T!!! Student 2
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 120 degrees, and the measure of angle UST is 15 ( x plus 2 ) degrees.
x = 6
Martin drew a pair of perpendicular lines and a pair of parallel lines. Which of these statements best compares the pairs of perpendicular and parallel lines?
Perpendicular lines are lines that intersect at right angles, and parallel lines are lines that never meet.
Is the figure an example of a line?
image of points A and B, which are connected by a finite number of points that do not continue forever in opposite directions
No, it has two endpoints.
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The endpoints of a segment are given. Find the length of the segment rounded to the nearest tenth. Then find the coordinates of the midpoint of the segment. F(1, 7) and G(6, 0)
You and your friend leave on different flights from the same airport. Determine which flight is farther from the airport. Explain your reasoning. Your flight: Flies 100 miles due west, then turns 20° toward north and flies 50 miles. Friend's flight: Flies 100 miles due north, then turns 30° toward east and files 50 miles.
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