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LEVEL 3: In the figure, RZ and WT are transversal of line s and t. If m∠ RVT = 5x + 6, m∠ VWY = 8x + 7, and m∠ WYZ = 16x - 8, find x.

x=7

x=14

No Solution

x=5.5

LEVEL 2: Make a conjecture for based on this information: For points P, Q, and R, PQ = 9, QR = 15, and PR = 12.

Forms a (right) triangle with a perimeter of 47 units. (Pythagorean Triple)

Forms a (right) triangle with a perimeter of 36 units. (Pythagorean Triple)

Forms a line with a length of 36 units.

Forms a line with a length of 47 units.

LEVEL 1: Determine the truth value of the following statement for each set of conditions... If it does not rain this Sunday, then we will have a picnic. a) It rains this Sunday, and we have a picnic.

LEVEL 1: Determine the truth value of the following statement for each set of conditions... If it does not rain this Sunday, then we will have a picnic. b) It rains on Sunday and we will not have a picnic.

LEVEL 1: Determine the truth value of the following statement for each set of conditions... If it does not rain this Sunday, then we will have a picnic. c) It doesn't rain this Sunday, and we have a picnic.

LEVEL 1: Determine the truth value of the following statement for each set of conditions... If it does not rain this Sunday, then we will have a picnic.d) It doesn't rain this Sunday, and we don't have a picnic.

LEVEL 1: Fill in the blanks of the truth table.

T,T,T,T,T,T,T,T

F,F,F,F,F,F,F,F

T,F,T,F,T,F,T,F

T,T,F,F,T,T,F,F

LEVEL 2: Decide what type of relationship the lines with the given equations have: \[y=\frac{1}{2}x+3\] \[y=\frac{1}{2}x-3\]

perpendicular

parallel

neither

LEVEL 2: \[GK bisects ∠FGH.\] If m∠FGH = 3v - 4 and m∠kgh = 2v+7, find v.

33

58

29

11

LEVEL 2: What are the steps for the following Triangle Proof? Given: WY ≅ XV, VW ┴ WX, YX ┴ WX ... Prove: ΔXWV ≅ ΔWXY

\[1.) WY ≅ XV , VW ┴ WX , YX ┴ WX\] 1.) Given \[2.) ∠VWX ≅ ∠YXZ\] 2.) Definition of Perpendicular Lines \[3.) ∠VWX and ∠YXZ = right angles\] 3.) Right Angle Congruency\[4.) WX ≅ WX\] 4.) Reflexive Property \[5.) ΔXWY ≅ ΔWXY\] 5.) SAS congruency

\[1.) WY ≅ XV , VW ┴ WX , YX ┴ WX\] 1.) Given \[2.) ∠VWX ≅ ∠YXZ\] 2.) Right Angle Congruency \[3.) ∠VWX and ∠YXZ = right angles\] 3.) Definition of Perpendicular Lines \[4.) WX ≅ WX\] 4.) Reflexive Property \[5.) ΔXWY ≅ ΔWXY\] 5.) SAS congruency

\[1.) WY ≅ XV , VW ┴ WX , YX ┴ WX\] 1.)Given \[2.) ∠VWX and ∠YXZ = right angles\] 2.) Definition of Perpendicular Lines \[3.) ∠VWX ≅ ∠YXZ\] 3.) Right Angle Congruency \[4.) WX ≅ WX\] 4.) Reflexive Property \[5.) ΔXWY ≅ ΔWXY\] 5.) Hypotenuse Leg congruency

\[1.) WY ≅ XV , VW ┴ WX , YX ┴ WX\] 1.)Given \[2.) ∠VWX and ∠YXZ\] are right angles 2.) Right Angle Congruency \[3.) ∠VWX ≅ ∠YXZ\] 3.) Definition of Perpendicular Lines \[4.) WX ≅ WX\] 4.) Reflexive Property \[5.) ΔXWY ≅ ΔWXY\] 5.) AAS congruency

LEVEL 1: Name all the planes intersecting plane CDI.

\[ABC, CBG, ADI, FGH\]

\[CBA, DAF, HGF\]

\[BAD, GFI, CBG, GFA\]

\[DAB, CBG, FAD\]

LEVEL 1: Name all the segments parallel to GF.

\[BC, AD, HI\]

\[AB, CD\]

\[AB, HI\]

\[AB, CD, HI\]

LEVEL 2: Conjecture: Adjacent angles are supplementary. (show counterexample)

Invalid

Valid

LEVEL 2: If m∠4 = 78°, and m∠6 = 78°, state weather these two lines are parallel or not. Why or why not?

parallel; (m∠2) 78°≅ (m∠6) 78°

not parallel; (m∠2) 78° + (m∠6) 78° ≠ 180

parallel; (m∠2) 78° + (m∠6) 78° = 156°

not parallel; (m∠2) 78° + (m∠6) 78° ≠ 156°

LEVEL 1:What type of angle pair is ∠4 and ∠6?

alternate interior

alternate exterior

consecutive interior

corresponding

no angle pair

LEVEL 2:What are the 6th and 7th step of this Isosceles Triangle Proof? Given: X is the midpoint of VW and VW ┴ UX ... Prove:∠V≅∠W.

6.) = ASA congruency ... 7.) =CPCTC

6.) = SSS congruency ... 7.) =CPCTC

6.) = CPCTC ... 7.) =SAS congruency

6.) = SAS congruency ... 7.) =CPCTC

LEVEL 2:What are the 3rd and 4th steps of this Isosceles Triangle Proof? Given: K is the midpoint of IJ, HJ ≅ HI

3rd = ΔHKI ≅ ΔHKJ (SSS concurrency), 4th = HI ≅ HJ (CPCTC)

3rd = IK ≅ KJ (Definition of midpoint), 4th = HI ≅ HJ (CPCTC)

3rd = HK ≅ HK (Reflexive Property), 4th = HI ≅ HJ (CPCTC)

3rd = IK ≅ KJ (Definition of midpoint), 4th = HK ≅ HK (Reflexive Property)

LEVEL 2:In the figure, line AB || CD. Find x and y. (HINT: Quadrilaterals have a angle sum of 360°. )

x = 32, y = 140

x = 140, y = 52

x = 52, y = 140

x = 38, y = 154

LEVEL 1:A line segment has the endpoints V(0, -5) and W(-2, 5). Find the coordinates of its midpoint.

M = (1, 2.5)

M = (2.5, 1)

M = (0, -1)

M = (-1, 0)

LEVEL 2:As shown in the figure below, ∆ABC is isosceles with the length of AB equal to the length of AC. The measure of ∠A is 40° and points B, C, and D are collinear. What is the measure of ∠ACD ?

70°

80°

110°

140°

160°

LEVEL 1: What is the length, in units of AC ?

5

3√5

3+√5

3√3

3√6

LEVEL 1: In the figure below, line m is parallel to line n, and line t is a transversal crossing both m and n. Which of the following lists has 3 angles that are all equal in measure?

∠a, ∠b, ∠d

∠a, ∠c, ∠d

∠a, ∠c, ∠e

∠b, ∠c, ∠d

∠b, ∠c, ∠e

LEVEL 3: Find the distance between these parallel lines. \[y=2x+7\] \[y=2x-3\]

5√3 units

5√2 units

3√5 units

2√5 units

LEVEL 1: Determine whether PQ and UV are parallel, perpendicular, and neither. *Find the slope and compare* ... P(0,3), Q(2,4), U(2,1), V(8,4)

LEVEL 1: Graph the line that satisfies the given condition: Slope = 2 and passes through (-1,3)

LEVEL 2: What are the 4th and 5th steps in this proof? Given: HI ≅ TU, IJ ≅ UV .... Proove: HJ ≅ TV

4.) = ST + LN = LN + NR (Segment Addition), 5.) = ST + LN [-LN] = LN [-LN] + NR (Subtraction)

4.) = ST + TU = LN + NR (Segment Addition), 5.) = ST = LN (Substitution)

4.) = ST + TU = LN + NR (Substitution), 5.) = ST + LN = LN + NR (Substitution)

4.) = ST + TU = LN + NR (Substitution), 5.) ST + TU = SU, LN + NR = LR (Segment Addition)

LEVEL 3: Sara places a ladder on level ground against a vertical wall. When the base of the ladder is 20 feet from the wall, the ladder reaches a height of 15 feet along the wall. Sara then moves the base 7 feet closer to the wall. To the nearest foot, how high up the wall does the ladder reach now. (*HINT:* It would be best to draw a picture of this problem.)

19 feet

21 feet

22 feet

24 feet

LEVEL 2: Given: ΔABC ≅ ΔDBC ; 2m∠CBD = m∠ABD ... Which best describes Δ ABD?

Isosceles

Right

Scalene

Equilateral

LEVEL 1: Find the percision for this measurement ... 60.3 km

60.8 km - 59.8 km

60.25 km - 60.35 km

60.4 km - 60.5 km

61.3 km - 59.3 km

LEVEL 1: Find the percision for this measurement ... 76 ft

75.5 ft - 75.6 ft

75.5 ft - 76.5 ft

75 ft - 77 ft

75.95 ft - 76.05 ft

LEVEL 1: If Johnny plots 275 points on a grid, how many lines can he make out of these points?

137 lines

274 lines

138 lines

550 lines

LEVEL 1: Select 2 of the following terms to complete the following sentence: Angles that are _________ are always __________.

Congruent Angles

Supplementary Angles

Complementary Angles

Vertical Angles

LEVEL 1: Find the missing endpoint if R is the midpoint of QS ... \[R(2,0) ; S(5,2)\]

Q = (1,3.5)

Q = (3.5,1)

Q = (3,2)

Q = (2,3)

LEVEL 1: Find the midpoint ... \[J(4,6) ; L(10,2)\]

K = (7,4)

K = (4,7)

K = (5,6)

K = (6,5)

LEVEL 2: Find the measure of each side of ΔABC with vertices \[A(1,5), B(6,1), and C(2,-6)\] Classify the triangle by it's sides.

Acute