MATH-G

HTH Roeser Triangles and Logic

Exam not valid for Paper Pencil Test Sessions

[Exam ID:10ZP6A

1 Part of a marching band formed a triangle made with trumpet players on one side, clarinet players on one side, and flute players on the third side. •The angle formed by the trumpet and flute players measured 45°. •The angle formed by the flute and clarinet players measured 68°.

Which orders the sides of this triangle from least to greatest using the instrument names?A Clarinet, trumpet, fluteB Clarinet, flute, trumpetC Trumpet, flute, clarinetD Flute, trumpet, clarinet

2

Which list has the sides of ΔABC ordered from longest to shortest?A BC, AC, ABB AB, AC, BCC BC, AB, ACD AC, AB, BC

3

Which lists the sides of ΔBCD in order from shortest to longest?A CD , BD , BCB BC , BD , CDC BD , CD , BCD BC , CD , BD

4 Three survey markers are located on a map at points H, I, and J. A triangle is formed

by connecting these markers by string so that HI = 150 feet, HJ = 245 feet, and IJ = 365 feet. Which statement is true about the measures of the angles of ΔHIJ? A m ∠I is the smallestB m ∠H is the smallestC m ∠I is the largestD m ∠H is the largest

5 In the triangle shown, GR = 11, BR = 8, and BG = 7.

Which statement is true about the angles in ΔRGB ?A m ∠G is the leastB m ∠R is the leastC m ∠G is the greatestD m ∠R is the greatest

6 Which could be the lengths of three sides of a triangle?

A 6 cm, 14, cm, 8 cmB 9 cm, 11 cm, 21 cmC 8.5 cm, 17 cm, 10.6 cmD 14 cm, 4.7 cm, 4.7 cm

7 Two sides of a triangle measure 14 inches and 8 inches. Which cannot be the length of

the remaining side?A 8 in.B 14 in.C 6 in.D 21 in.

8 John wants to make a triangular garden. Which of the following are possible

dimensions?A 8 ft by 12 ft by 20 ftB 6 ft by 6 ft by 12 ftC 6 ft by 8 ft by 10 ftD 4 ft by 5 ft by 10 ft

9 Directions: Click and drag each selected number to the correct box.

The lengths of two sides of a triangle are 24 inches and 43 inches. What is the range of possible lengths, in inches, for the third side, x , of this triangle?

19 67

10 Jennifer made these measurements on ΔABC . BC must be —

A less than 10 inchesB between 12 and 22 inchesC greater than 22 inchesD between 10 and 12 inches

11

The locations of three water pumping stations form a triangle on a map of the area. The distance from station A to station B is 650 meters. The distance from station B to station C is 558 meters. The distance from station A to station C is—A less than 92 mB greater than 1,208 mC exactly 92 mD between 92 m and 1,208 m

12

Using the information given, which congruence postulate or theorem can be used to prove that ΔPQR ≅≅≅≅ ΔTSR ?A Side-Side-Side PostulateB Side-Angel-Side PostulateC Hypotenuse-Leg TheoremD Angle-Angle-Side Theorem

13 Triangles ABE , ADE , and CBE are shown on the coordinate grid, and all the vertices

have coordinates that are integers.

Which statement is true?A No two triangles are congruent.B Only ΔABE and ΔCBE are congruent.C Only ΔABE and ΔADE are congruent.D Triangle ABE , ΔADE , and ΔCBE are all congruent.

14 Given the measures shown in the diagram, which two triangle are congruent?

A Q and SB R and TC R and SD Q and T

15 Directions: Click and drag each selected reason to the correct box.

Given: Figure ABCD with diagonal AC AB ≅≅≅≅ DC ; BC ≅≅≅≅ AD

Complete the proof of ΔABC ≅≅≅≅ ΔCDA by selecting the reasons for the last two statements.

16 Given: In this figure, AC and BD bisect each other.

Based on the information given, which triangle congruence theorem could be used to prove ΔAED ≅≅≅≅ ΔCEB ?A Side-Angle-Side (SAS)B Angle-Side-Angle (ASA)C Angle-Angle-Side (AAS)D Side-Side-Side (SSS)

Reflexive property

Side-Side-Side (SSS) Theorem

17 Coordinates A (2,5), B (6,4) and C (6,0) are connected to form ΔABC.

If ΔCDA is congruent to ΔABC, what are the coordinates of D?A (1,1)B (2,2)C (1,2)D (2,1)

18 With the information given in the drawings, which pair of triangles can be proven

congruent by the Side-Angle-Side postulate?

A

B

C

D

19 Given: Q lies on PR and S lies on RT

Which condition proves ΔPRT ~ ΔQRS ?A ∠PQS ≅ ∠TSQB ∠PTR ≅ ∠TPR

C = QS PT

QR SR

D = QS PR

SR TR

20

Look at this triangle.

Which triangle is similar to the given triangle?

A C

B D

21 Three triangles that do not overlap are shown on the coordinate grid. The

coordinates of all vertices are integers.

Which statement is true?A ΔABD ~ ΔEBAB ΔABD ~ ΔDBCC ΔCBD ~ ΔABED ΔCBD ~ ΔEBA

22

A 22B 11C 12D 24

23 Which is a valid conclusion that can be drawn from these statements?

If a quadrilateral is a rhombus, then it is a parallelogram. If a quadrilateral is a parallelogram, then its opposite angles are congruent.

A Every quadrilateral is a rhombus.B Every parallelogram is a rhombus.C Opposite angles of a rhombus are congruent.D Opposite angles of a quadrilateral are congruent.

24 Which Venn diagram represents all the following set of statements?

• Some triangles are acute. • Some triangles are obtuse. • No triangle is both acute and obtuse. • Some acute triangles are equilateral.

A C

B D

25 In which group of statements is the conclusion not justified by the previous pair of

statements?

A All squares are rectangles. All rectangles are parallelograms. All squares are parallelograms.

B All fish live in the water. Some snakes live in the water. Some snakes are fish.

C All dinosaurs are extinct. A triceratops is a dinosaur. All triceratops are extinct.

D All cooks work in the kitchen. Mary is a cook. Mary works in the kitchen.

26 Directions: Click on a box to choose each answer you want to select. You must select all correct answers.

This Venn diagram represents students who play instruments in the orchestra.

Identify each region of the Venn diagram that represents students who play only the flute and the oboe.

Region 1 Region 3 Region 6 Region 9 Region 11

Region 2 Region 4 Region 7 Region 10 Region 13

27 Let p represent

x 2 = 21,

and let q represent x is not a whole number.

Which is a representation of the statement below? If x is a whole number, then x 2 ≠ 21

A p → ∼ qB ∼ q → ∼ pC ∼ p → ∼ qD ∼ p → q

28

Which of the following statements must be true about this Venn diagram?A Some rhombi are rectangles.B All rectangles are rhombi.C All quadrilaterals are rhombi and rectangles.D Quadrilaterals are not rhombi or rectangles.

29 Given the following measures of the sides of triangles, which is a right triangle?

A 45 yd, 35 yd, 25 ydB 52 in., 50 in., 11 in.C 45 ft, 40 ft, 35 ftD 41 cm, 40 cm, 9 cm

30 Let p = An equation is of the form y = mx + b .

Let q = Its graph is a line. Argument: If an equation is of the form y = mx + b , then its graph is a line. The graph is not a line. Therefore, the equation is not of the form y = mx + b.

Which of the following is the symbolic representation of the given argument?

A

B

C

D

31 Consider the following statement.

If 4 x = 8, then x = 2.

Which is the inverse of the statement?A If x = 2, then 4x ≠ 8.B If 4x ≠ 8, then x ≠ 2.C If x = 2, then 4x = 8.D If x ≠ 2, then 4x ≠ 8.

32 Which is the inverse of the following statement?

If the measure of an angle is 90°, then it is a right angle.

A If the measure of an angle is not 90°, then it is not a right angle.B If the measure of an angle is not 90°, then it is a right angle.C If an angle is not a right angle, then its measure is not 90°.D If an angle is not a right angle, then its measure is 90°.

33 Let p represent

Two angles are vertical angles.

Let q represent The angles are congruent.

What is the symbolic representation of the following statement? If two angles are congruent, then the angles are vertical angles.

A q → pB p → qC ~q → ~ pD ~p → ~q

34 Which drawing contains a pair of similar triangles?

A

B

C

D

35 Statement: If lines are skew, then they are not coplanar.

What is the contrapositive of the statement?A If lines are not skew, then they are coplanar.B If lines are skew, then they are coplanar.C If lines are coplanar, then they are not skew.D If lines are not coplanar, then they are skew.

36 Joseph is standing 12 feet from a mirror lying on the ground, and his eyes are 5 feet

above the ground.

The line-of-sight reflection on the mirror makes ∠∠∠∠1 congruent to ∠∠∠∠2 .If the building is 264 feet from the mirror, which is closest to the height of the building?A 130 ftB 100 ftC 145 ftD 110 ft

37

What value of x makes ΔDEF ≅≅≅≅ ΔJLK ?A x = 9.4B x = 6.0C x = 4.1D x = 5.3

38 Which of the following sets of lengths can represent the measures of the sides of a

right triangle?A 4, 5, 6B 5, 12, 15C 8, 10, 17D 20, 21, 29

39 Mr. Ammons is constructing a walkway through his rectangular garden. The walkway

runs diagonally as shown in the diagram.

Which is closest to the length of the walkway?A 28.3 ftB 30.0 ftC 18.7 ftD 39.0 ft

40 A spectator is viewing the six cars of a roller coaster as it travels down a hill at an

amusement park.

Which is closest to the total length of the six cars?A 12.3 ftB 15.8 ftC 25.6 ftD 32.5 ft

41 A drawing of Mark’s kite is shown below.

What is the length of the short section of the outer frame indicated by x in the drawing?A 16 in.B 15 in.C 13 in.D 14 in.

42 Triangle ABC is an equilateral triangle with side lengths of 10 inches.

What is the length, in inches, of AD ?

A 10√3 3

B 5√2C 5D 5√3

43

In the figure, what is the value of x ?A 6√3B 6√2C 6D 12

44 An equilateral triangle is folded in half.

What is x , the height of the equilateral triangle?A 14√3 cmB 14 cmC 7√3 cmD 7 cm

45 Reuben attached a wire between two poles on a hill as shown.

Which is the closest to x , the distance between the two poles?A 27 ftB 29 ftC 60 ftD 75 ft