Geometry Unit 3 Answers PHS

(L2) Given: ℓ ∣∣ m, cut by transversal t Prove: ∠1 is supplementary to ∠7

1. H 3. B 5. A 6. E 7. I

(L5) Choose the correct definition of the term slope.

the ratio of the rise to the run of a line in a coordinate plane.

(L1) A _____ line is a line that intersects two coplanar lines at two different points.

transversal

(Q1) A line that intersects two coplanar lines at two different points is called a _____.

transversal line

(PT) Choose whether the slope of the line is positive, negative, zero, or undefined. (vertical)

undefined

(L2) ∠2 and ∠3 are ______ ∠s, so they are ______.

vertical; congruent

(L6) Find the slope and y-intercept for each linear equation and determine if the graphs of the pair are parallel, perpendicular, concurrent (but not perpendicular), or coincident. x=3y+9 x/3=-y+2 The lines are __________.

x=3y+9 slope = 1/3 y -intercept = -3 x/3=-y+2 slope = -1/3 y -intercept = 2 The lines are concurrent.

(PT) pairs of angles formed when a transversal intersects two lines so that they lie on opposite sides of the transversal and outside the lines

Alternate exterior angles

(L3) The Converse of the Corresponding Angles Postulate states that: _____

If two coplanar lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

(Q3) Given: Point A(5,-2) on a line with m=undefined. Which of these points could be on the line?

J (5, 1)

(L1) Which pair of lines are perpendicular?

MN↔ and MQ↔

(L1) Which pair of lines is concurrent?

MN↔ and MQ↔

(L1) Which pair of lines is parallel?

MN↔ and PO↔

(L1) Which pair of lines is skew?

MN↔ and RS↔

(PT) Which lines are perpendicular?

MQ↔ and MN↔

(L5) Given: Point B(3,-4) on a line with m=undefined. Which of these points could be on the line?

N(3,0)

(PT) Which lines are skew?

OS↔ and QT↔

(L1) _____ lines intersect to form 90° angles.

Perpendicular

(L1) _____ lines are lines that do not lie in the same plane and have no points in common

Skew

(PT) _____ is the ratio of the rise to the run of a line in a coordinate plane.

Slope

(L1) Main St. and Hwy 442 are _____.

coincident

(L4) Theorem 3.4A states: If two _____ lines form a linear pair of congruent angles, then the lines are perpendicular.

intersecting

(PT) Choose whether the slope of the line is positive, negative, zero, or undefined. (diagonal right)

negative

(Q3) Choose whether the slope of the line is positive, negative, zero, or undefined. (diagonal right)

negative

(Q2) An informal proof in which the statements and reasons are written as sentences in a paragraph is called a _____.

paragraph proof

(L1) Elm Ave. and Walnut Ave. are _____.

parallel

(Q1) Lines that lie in the same plane but have no points in common are called _____.

parallel lines

(L5) Choose whether each slope is positive, negative, zero, or undefined.

(diagonal right): negative { \ } (diagonal left): positive { / } (vertical): undefined { | } (horizontal): zero { — }

(L6) The Perpendicular Lines Theorem states that in a coordinate plane, two non-vertical lines are perpendicular if, and only if, the product of their slopes is _____.

-1

(L5) Find the slope of AB↔.

1

(L3) Given: lines ℓ and m cut by transversal, t, alternate exterior angles ∠1≅∠8 Prove: ℓ ∥ m

1. (Stmnt): A 1. (Rsn): F 2. (Rsn): G 3. (Stmnt): B 3. (Rsn): C

(Q2) Given: ∠6≅∠3 Prove: ℓ∥m

1. C 2. D 3. F

(L2) Given: ℓ ∣∣ m, cut by transversal t Prove: ∠2≅∠7

1. F 2.B 3. D 4.A

(Q2) Which theorem or postulate is stated? If two coplanar lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel

Converse of the Alternate Interior Angles Theorem

(Q2) Which theorem or postulate is stated? If two coplanar lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

Converse of the Corresponding Angles Postulate

(Q2) Which theorem or postulate is stated? If two coplanar lines are cut by a transversal so that the same-side exterior angles are supplementary, then the lines are parallel.

Converse of the Same-Side Exterior Angles Theorem

(Q2) Which theorem or postulate is stated? If two coplanar lines are cut by a transversal so that same-side interior angles are supplementary, then the lines are parallel.

Converse of the Same-Side Interior Angles Theorem

(Q1) Which theorem or postulate shows that ∠4≅∠8?

Corresponding Angles Postulate

(Q2) Which theorem or postulate is stated? If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

Corresponding Angles Postulate

(PT) pairs of angles formed when a transversal intersects two lines so that they lie on the same side of the transversal and on the same side of the lines

Corresponding angles

(L5) Given: Point C (2, 3) on a line with m=1 Which of these points could be on the line?

D (3, 4)

(Q3) Given Point C (3, 1) on a line with slope m=3 Which point could be on the line?

D (4, 4)

(L2) Which pair of angles are same-side exterior angles? Are they congruent or supplementary?

E; D

(L5) Given: Point A (1, 2) on a line with m=0 Which of these points could be on the line?

F (3, 2)

(L5) Given: Point D (2, 5) on a line with m=-3 Which of these points could be on the line?

F (3, 2)

(Q3) In a coordinate plane, two nonvertical lines are parallel if, and only if, they have the same slope is a statement of the _____.

Parallel Lines Theorem

(Q3) In a coordinate plane, two nonvertical lines are perpendicular if, and only if, the product of their slopes is -1 is a statement of the _____.

Perpendicular Lines Theorem

(Q1) Which lines are skew?

QR↔ and PT↔

(Q1) Which lines are concurrent?

RS↔ and OS↔

(Q1) Which lines are parallel?

RS↔ and QT↔

(PT) _____ is the difference in y -values between the coordinates of two points.

Rise

(PT) _____ is the difference in x -values between the coordinates of two points.

Run

(Q2) Which theorem or postulate is stated? If two parallel lines are cut by a transversal, then the same-side exterior angles are supplementary.

Same-Side Exterior Angles Theorem

(Q1) Which theorem or postulate shows that ∠6 is supplementary to ∠4?

Same-Side Interior Angles Theorem

(Q2) Which theorem or postulate is stated? If two parallel lines are cut by a transversal, then the same-side interior angles are supplementary.

Same-Side Interior Angles Theorem

(L2) ∠4 and ∠6 are ______ angles, so they are ______.

Same-Side Interior; Supplementary

(PT) pairs of angles formed when a transversal intersects two lines so that they lie on the same side of the transversal and between the lines

Same-side interior angles

(PT) Which lines are parallel?

TS↔ and QR↔

(L1) Lines that lie in the same plane but have no points in common are called _____ lines.

parallel

(L3) If two lines are cut by a transversal such that their alternate interior or alternate exterior angles are congruent, then the lines are _____.

parallel

(L4) The Perpendicular Transversal Theorem states: In a plane, if two _____ lines are cut by a transversal such that the transversal is perpendicular to one of the lines, then it is perpendicular to the other line.

parallel

(L4) Theorem 3.4C states: If two coplanar lines are perpendicular to the same line, then the two lines are _____.

parallel

(L1) Pine St. and Main St. are _____.

perpendicular

(PT) A line or line segment perpendicular to a line segment at the midpoint of the segment is a _____.

perpendicular bisector

(Q1) Lines that intersect to form 90° angles are called _____.

perpendicular lines

(PT) Choose whether the slope of the line is positive, negative, zero, or undefined. (diagonal left)

positive

(Q3) Choose whether the slope of the line is positive, negative, zero, or undefined. (diagonal left)

positive

(Q3) The difference in y -values between the coordinates of two points on a line is called the _____.

rise

(Q3) The difference in x -values between the coordinates of two points on a line is called the _____.

run

(L1) Pairs of angles formed when a transversal intersects two lines so that they lie on the same side of the transversal and outside the lines are called _____.

same-side exterior angles

(L1) Pairs of angles formed when a transversal intersects two lines so that they lie on the same side of the transversal and between the lines are called _____.

same-side interior angles

(Q1) Pairs of angles formed when a transversal intersects two lines so that they lie on the same side of the transversal and between the lines are called _____.

same-side interior angles

(Q1) Lines that do not lie in the same plane and have no points of intersection are called _____.

skew lines

(L6) The Parallel Lines Theorem states that in a coordinate plane, two non-vertical lines are parallel if, and only if, they have the same _____.

slope

(Q3) The ratio of the rise to the run of a line in a coordinate plane is called the _____.

slope

(L3) If two lines are cut by a transversal such that their same-side exterior angles are _____, then the lines are parallel.

supplementary

(L3) If two lines are cut by a transversal such that their same-side interior angles are _____, then the lines are parallel.

supplementary

(L5) Choose the correct definition of the term run.

the difference in x-values between the coordinates of two points on a line.

(L5) Choose the correct definition of the term rise.

the difference in y-values between the coordinates of two points on a line.

(L5) What is the slope of a surface having a rise of 5 feet and a run of 0 feet?

undefined

(Q3) Choose whether the slope of the line is positive, negative, zero, or undefined. (line is vertical)

undefined

(L6) Find the slope and y-intercept for each linear equation and determine if the graphs of the pair are parallel, perpendicular, concurrent (but not perpendicular), or coincident. y=2x+3 y=-1/2x+1 The lines are __________.

y=2x+3 slope = 2 y -intercept = 3 y=-1/2x+1 slope = -1/2 y -intercept = 1 The lines are perpendicular.

(PT) Find the slope and y-intercept for each linear equation and determine if the graphs of the pair are parallel, perpendicular, concurrent (but not perpendicular), or coincident. y=3x+7 y=-1/3x-2

y=3x+7 slope = 1 y-intercept = 7 y=-1/3x-2 slope = -1/3 y-intercept = -2 The lines are perpendicular

(L6) Find the slope and y-intercept for each linear equation and determine if the graphs of the pair are parallel, perpendicular, concurrent (but not perpendicular), or coincident. y=4x-2 y=-2x+4 The lines are __________.

y=4x-2 slope = 4 y -intercept = -2 y=-2x+4 slope = -2 y -intercept = 4 The lines are concurrent.

(L6) Find the slope and y-intercept for each linear equation and determine if the graphs of the pair are parallel, perpendicular, concurrent (but not perpendicular), or coincident. y=5x-7 y=5x-3 The lines are __________.

y=5x-7 slope = 5 y -intercept = -7 y=5x-3 slope = 5 y -intercept = -3 The lines are parallel.

(PT) Choose whether the slope of the line is positive, negative, zero, or undefined. (horizontal)

zero

(Q3) Choose whether the slope of the line is positive, negative, zero, or undefined. (horizontal)

zero

(PT) Which are same-side exterior angles?

∠1 ∠7

(PT) Which are alternate exterior angles?

∠1 ∠8

(Q1) Which are same-side exterior angles?

∠1 and ∠7

(Q1) Which are alternate exterior angles?

∠1 and ∠8

(PT) Which are same-side interior angles?

∠3 ∠5

(Q1) Which are same-side interior angles?

∠3 and ∠5

(PT) Which are corresponding angles?

∠4 ∠8

(Q1) Which are alternate interior angles?

∠4 and ∠5

(L1) Which pair of angles are corresponding angles?

∠5 and ∠1

(L1) Which pair of angles are alternate interior angles?

∠5 and ∠4

(L1) Which pair of angles are same-side interior angles?

∠6 and ∠4

(Q1) Which is the corresponding angle for ∠3 ?

∠7

(L1) Which pair of angles are alternate exterior angles?

∠7 and ∠2

(L1) Which pair of angles are same-side exterior angles?

∠8 and ∠2

(L5) What is the run of a 50% slope with a rise of 50 feet?

100 feet

(L3) Given: lines ℓ and m cut by transversal, t; ∠2 is supplementary to ∠8 . Prove: ℓ ∥ m

2. (Rsn): D 4. (Stmnt): G 5. (Stmnt): A 6. (Rsn): F 7. (Stmnt): I 8. (Rsn): B

(PT) Given: ℓ∥m , cut by transversal t ; m∠2=130° Prove: m∠8=50°

2. A 4. F 5. D

(L4) Given: Line m intersects line ℓ; ∠1≅∠2 . Prove: m∠1=90° and m∠2=90°

2. C 3. A

(Q2) Given: ∠3 and ∠5 are supplementary. Prove: ℓ∥m

2. C 3. B 4. D

(L4) Given: t intersects ℓ and m ; t⊥ ℓ;ℓ ∥m . Prove: m∠5=m∠6

2. C 4. B

(Q1) Given: ℓ ∣∣ m, cut by transversal t; m∠6=130° Prove: m∠3=130°

3. (F) Alternate Interior Angles Theorem 5. (B) m∠3=130°

(PT) Given: ℓ∥m , cut by transversal t ; ∠4 and ∠6 are same-side interior angles. Prove: ∠4 and ∠7 are supplementary angles.

3. [E] 5. [C] 7. [A]

(Q3) Find the slope and y-intercept for each linear equation and determine if the graphs of the pair are parallel, perpendicular, concurrent (but not perpendicular), or coincident. 3x=y+7 2y=6x-6

3x=y+7 slope = 3 y-intercept = -7 2y=6x-6 slope = 3 y-intercept = -3 The lines are parallel

(L1) What is the measure of the angle formed by the intersection of MN↔ and MQ↔ ?

90°

(L2) Which angle forms an alternate exterior angle with ∠1? Are the two angles congruent, or supplementary?

A; E

(L1) _____ lines intersect and have only one point in common.

Concurrent

(PT) lines that intersect and have only one point in common

Concurrent lines

(Q2) Which theorem or postulate is stated? If two coplanar lines are cut by a transversal, so that alternate exterior angles are congruent, then the lines are parallel.

Converse of the Alternate Exterior Angles Theorem

(Q3) Find the slope and y-intercept for each linear equation and determine if the graphs of the pair are parallel, perpendicular, concurrent (but not perpendicular), or coincident. y=-5x+2 y=1/5x-2

y=-5x+2 slope = -5 y-intercept = 2 y=1/5x-2 slope = 1/5 y-intercept = -2 The lines are perpendicular

(PT) Find the slope and y-intercept for each linear equation and determine if the graphs of the pair are parallel, perpendicular, concurrent (but not perpendicular), or coincident. y=3x+4 9x=3y-6

y=3x+4 slope = 3 y-intercept = 4 9x=3y-6 slope = 3 y-intercept = 2 The lines are parallel

(L6) Find the slope and y-intercept for each linear equation and determine if the graphs of the pair are parallel, perpendicular, concurrent (but not perpendicular), or coincident. 4y=8x-2 -4x+2y=-1 The lines are __________.

4y=8x-2 slope = 2 y -intercept = -1/2 -4x+2y=-1 slope = 2 y -intercept = -1/2 The lines are coincident.

(Q1) Which theorem or postulate shows that ∠1≅∠8?

Alternate Exterior Angles Theorem

(Q2) Which theorem or postulate is stated? If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.

Alternate Exterior Angles Theorem

(L2) Which theorem or postulate shows that ∠3≅∠6?

Alternate Interior Angles Theorem

(Q1) Which theorem or postulate shows that ∠4≅∠5?

Alternate Interior Angles Theorem

(Q2) Which theorem or postulate is stated? If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

Alternate Interior Angles Theorem

(PT) pairs of angles formed when a transversal intersects two lines so that they lie on opposite sides of the transversal and between the lines

Alternate interior angles

(Q1) Which theorem or postulate shows that ∠6≅∠7?

Vertical Angles Theorem

(Q2) Which theorem or postulate is stated? Vertical angles are congruent.

Vertical Angles Theorem

(L1) Pairs of nonadjacent angles formed when a transversal intersects two lines so that they lie on opposite sides of the transversal and outside the lines are called _____.

alternate exterior angles

(Q1) Pairs of nonadjacent angles formed when a transversal intersects two lines so that they lie on opposite sides of the transversal and outside the lines are called _____.

alternate exterior angles

(L1) Pairs of angles formed when a transversal intersects two lines so that they line on opposite sides of the transversal and between the lines are called _____.

alternate interior angles

(Q1) Pairs of angles formed when a transversal intersects two lines so that they lie on opposite sides of the transversal and between the lines are called _____.

alternate interior angles

(L1) Lines that lie on top of one another and have all points in common are called _____ lines.

coincident

(Q1) Lines that lie one on top of the other and have all points in common are called _____.

coincident lines

(L1) What is the relationship between Cherry Blvd. and Elm Ave.?

concurrent

(Q1) Lines that intersect and have only one point in common are called _____.

concurrent lines

(L2) ∠1 and ∠5 are ______ angles.

congruent

(L1) Pairs of angles formed when a transversal intersects two lines so that they lie on the same side of the transversal and on the same sides of the lines are called _____.

corresponding angles

(Q1) Pairs of angles formed when a transversal intersects two lines so that they lie on the same side of the transversal and on the same side of the lines are called _____.

corresponding angles