Name: ________________________________________________ Period: ____________

Geometry Honors: Midterm Exam Review January 2019

The midterm will cover Chapters 1-6. You WILL NOT receive a formula sheet, but you need to know the following formulas – Make sure you memorize them!!

- Distance - Midpoint - Slope - Slope-Intercept Form

The exam is 1 hour and 55 minutes.

- 40 multiple choice questions (60 points) - 6 open ended questions (40 points)

It is YOUR responsibility to properly prepare for the midterm exam. Each day of exams is a half day. There is no homeroom - report directly to the first exam of the day. You will have a 10 minute break between exams. You may wish to use this time to use the bathroom or have a light snack. You will not be allowed to leave the classroom during exams.

CHAPTER 1: TOOLS OF GEOMETRY

1. Which figure shows 𝐴𝐵 ⃡ and point G contained in plane R?

F G

H J

2. Name the intersection of 𝐴𝐸 ⃡ and 𝐶𝐺 ⃡ .

A line CD C point C

B line AB D point G

3. If point P is between A and M, which is true?

A PA + AM = PM C AM + PM = AP

B AM + AP = PA D AP + PM = AM

4. Find the distance between A(–3, 5) and B(4, 2), to the nearest hundredth.

A 6.75 B 7.62 C 8.06 D 10

5. Find EF if E is the midpoint of 𝐷𝐹̅̅ ̅̅ , DE = 15 – 3x, and EF = x + 3.

F 1 G 3 H 6 J 9

6. Find the coordinates of B if A has coordinates (3, 5) and Y(–2, 3) is the midpoint of AB.

A B (–7, 1) B B (3, 3) C B (5, –2) D B (–7, –3)

7. Find the length of 𝑋𝑍̅̅ ̅̅ if Y(–4, 4) is the midpoint of 𝑋𝑍̅̅ ̅̅ and X has coordinates (2, –4).

For Questions 8-10, use the figure.

8. What is another name for ∠2?

A ∠WYX C ∠WXY

B ∠3 D ∠Y

9. Which angles form a linear pair?

F ∠1 and ∠3 H ∠2 and ∠5

G ∠2 and ∠3 J ∠1 and ∠4

10. Name the angle that is vertical to ∠3.

A ∠1 B ∠2 C ∠3 D ∠4

11. If m∠HJK = 7y – 2 and m∠PQR = 133, find the value of y so that ∠HJK is supplementary to ∠PQR.

F –3 G 2 H 4 J 7

12. The measure of the complement of ∠A is 185 less than two times the measure of the supplement of ∠A.

Find m∠A.

13. In the figure, 𝑄𝑃 and 𝑄𝑇 are opposite rays. Find m∠PQR, m∠RQS, and m∠SQT. Then classify each

angle as right, acute, or obtuse.

For questions 14 and 15, use the figure below. 𝑯𝑳 bisects ∠KHI and 𝑯𝑮 and 𝑯𝑰 are opposite rays.

14. If ∠1 ≅ ∠2, m∠KHG = 70, and m∠1 = 3d + 2, find the value of d.

15. If m∠2 = a + 15 and m∠3 = a + 35, find the value of a so that 𝐻𝐿 ⊥ 𝐻𝐽 .

16. Which is not a polygon?

F G H J

17. Name this polygon by its number of sides and then classify it as convex or concave and regular or irregular.

18. Find the length of one side of a regular hexagon whose perimeter is 75 feet.

F 25 ft G 18.75 ft H 15 ft J 12.5 ft

19. Find the perimeter of a regular octagon if one of its sides is x + 6 and another side is 14 – x.

A 4 B 40 C 8 D 80

CHAPTER 2: REASONING AND PROOF

1. Make a conjecture about the next letter in the sequence.

L M N P Q R T . . .

2. Find a counterexample for the statement.

Five is the only whole number between 4.5 and 6.1.

3. Which statement has the same truth value as 3 = 5?

A 3 = x C AB = BC

B AB = 3 D BC = 3 + x

4. Determine whether the following statement is always, sometimes, or never true.

Points X, Y, and Z determine two lines.

5. If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then which is a valid conclusion?

I m∠1 = m∠2

II ∠1 ≅ ∠3

III m∠1 + m∠2 = m∠3

F I, II, and III G II only H I and II J I and III

For Questions 6 and 7, name the property that justifies the given statement.

6. If AB = CD and CD = 11, then AB = 11.

A Transitive B Symmetric C Congruence D Reflexive

7. If ∠XYZ ≅ ∠PQR, then ∠PQR ≅ ∠XYZ.

F Transitive G Symmetric H Congruence J Reflexive

8. Given: 𝑥 + 3 = 15𝑥 − 53

Prove: 𝑥 = 4

9. If B is in the interior of ∠DEF, m∠DEB = 27.2, and m∠DEF = 92.5, find m∠BEF.

10. If ∠1 is supplementary to ∠2 and ∠3 is complementary to ∠2, find m∠3 if m∠1 is 145.

A 35 C 55

B 45 D 90

11. Refer to the following figure to answer the questions below.

a. Name a pair of supplementary angles.

b. Name a pair of complementary angles.

c. Find m∠RUV.

12. Given: ∠1 ≅ ∠2

Prove: 𝑚∠𝐴𝐵𝐶 = 2(𝑚∠1)

CHAPTER 3: PARALLEL AND PERPENDICULAR LINES

For Questions 1-3, use the figure below.

1. What type of angles are ∠3 and ∠10?

F alternate interior angles

G alternate exterior angles

H corresponding angles

J consecutive interior angles

2. State the transversal that forms ∠11 and ∠13.

A ℓ B m C p D q

3. If m∠1 = 120, find m∠8.

F 60 G 110 H 120 J 140

4. Find m∠HJK.

A 33 C 78

B 45 D 147

5. Find the value of x so that 𝒦 ║ ℓ.

6. Find the value of x so that ℓ ║ m.

7. Two lines ℓ and k are cut by a transversal forming two pairs of alternate interior angles: ∠4 and ∠5 and

∠3 and ∠6. Which condition below is necessary to make lines ℓ and k parallel?

F ∠4 ≅ ∠3 H ∠4 ≅ ∠5 and ∠3 ≅ ∠6

G m∠3 + m∠6 = 180 J m∠3 + m∠6 = 90

8. If 𝐽𝐾̅̅ ̅ || 𝐿𝑀̅̅ ̅̅ , then ∠4 must be supplementary to ∠__ ?

9. Given: ∠1 and ∠3 are supplementary

Prove: 𝑗 ∥ 𝑘

10. Find the slope of the line that passes through points A(–7, 14) and B(5, –2).

F – 4

3 G –

3

4 H

3

4 J

4

3

11. Find the slope of a line parallel to 3y – 6x = 9.

12. Determine whether 𝑄𝑅 ⃡ and 𝑆𝑇 ⃡ are parallel, perpendicular, or neither for Q(–4, –4), R(5, 2), S(4, –5),

and T(0, 1).

13. Find the distance between two lines that have equations y = 3x + 1 and y = 3x – 19.

14. Find the distance from 𝐴(−1,5) to the line whose equation is 4𝑥 − 5𝑦 = 12.

CHAPTER 4: CONGRUENT TRIANGLES

1. Classify △DEF with vertices D(2, 3), E(5, 7) and F(9, 4).

F acute G equiangular H obtuse J right

2. Find PR if △PQR is isosceles, ∠Q is the vertex angle, PQ = 4x – 8, QR = x + 7, and PR = 6x – 12.

3. In the figure, ∠1 ≅ ∠2. Find the measures of the numbered angles.

4. Find m∠PQR.

5. If m∠D = 42, what is m∠E?

A 18 C 43

B 40 D 81

6. If PQ = QS, QS = SR, and m∠R = 20, find m∠PSQ.

7. Let △ABC be an isosceles triangle with △ABC ≅ △PQR. If m∠B = 154, find m∠R.

F 154 G 126 H 26 J 13

8. If △ABC ≅ △WXY, AB = 72, BC = 65, CA = 13, XY = 7x – 12, and WX = 19y + 34, find the values of x

and y.

9. In the figure, 𝐿𝐾̅̅ ̅̅ bisects ∠JKM and ∠KLJ ≅ ∠KLM. Determine which theorem or postulate can be used

to prove that △JKL ≅ △MKL.

10. Which postulate or theorem can be used to prove △ABD ≅ △CBD?

A SAS C SSS

B ASA D AAS

11. Which of the following theorems can be used to prove △ABC ≅ △DEC?

A SSS C SAS

B AAS D ASA

12. Given: 𝐴𝐵̅̅ ̅̅ ∥ 𝐷𝐸̅̅ ̅̅ , 𝐴𝐷̅̅ ̅̅ bisects 𝐵𝐸̅̅ ̅̅

Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐶

13. Given: ∠1 ≅ ∠2, ∠3 ≅ ∠4, ∠5 ≅ ∠6, ∠7 ≅ ∠8

Prove: ∠𝐴 ≅ ∠𝐶

14. △PQR is an isosceles triangle with base 𝑄𝑅̅̅ ̅̅ . If m∠P = 6x + 40 and m∠Q = x – 10, find x.

F 20 G 25 H 30 J 100

15. Given: ∆𝐴𝐶𝐷 is isosceles with vertex A

𝐵𝐶̅̅ ̅̅ ≅ 𝐷𝐸̅̅ ̅̅

Prove: ∆𝐴𝐵𝐸 is isosceles

16. Find the coordinates of B, the midpoint of 𝐴𝐶̅̅ ̅̅ , if A(2a, b) and C(0, 2b).

F (2a, 2b) G (a, b) H (𝑎,3

2𝑏) J (

3

2 𝑎, 𝑏)

17. Write a coordinate proof showing that the segments joining the midpoints of the sides of a right triangle

form a right triangle.

CHAPTER 5: RELATIONSHIPS IN TRIANGLES

1. In △XYZ, which type of line is ℓ ?

F perpendicular bisector H altitude

G angle bisector J median

2. If 𝑅𝑉̅̅ ̅̅ is an angle bisector, find m∠UVT.

A 10 C 68

B 34 D 136

3. If 𝐵𝐷 is an altitude of △ABC, find the value of x.

For Questions 4 and 5, refer to the figure.

4. Find the value of a and m∠ZWT if 𝑍𝑊̅̅ ̅̅ ̅ is an altitude of △XYZ, m∠ZWT = 3a + 5, and

m∠TWY = 5a + 13.

5. Determine which angle has the greatest measure: ∠YWZ, ∠WZY, or ∠ZYW.

6. In △XYZ, point M is the centroid. If XM = 8, find the length of 𝑀𝐴.

7. The vertices of △ABC are A(–2, 3), B(4, 3), and C(–2, –3). Find the coordinates of each of the following

points of concurrency of △ABC.

a. circumcenter

b. orthocenter

For Questions 8 and 9 refer to the figure.

8. Which line segment is the shortest?

F 𝑃𝑄 H 𝑄𝑅

G 𝑅𝑆 J 𝑃𝑆

9. Which line segment is the longest?

A 𝑃𝑄 B 𝑄𝑅 C 𝑅𝑆 D 𝑃𝑆

10. Find x and the measure of each angle. Then list the sides of the triangle in order from shortest to

longest.

11. Which of the following sets of numbers cannot be lengths of the sides of a triangle?

A 1, 2, 3 B 2, 3, 4 C 3, 4, 5 D 4, 5, 6

12. The measures of two sides of △ABC are 19 and 15. The range for measure of the third side n would be

4 < n < ? .

13. Determine whether 128 feet, 136 feet, and 245 feet can be the lengths of the sides of a triangle.

14. Write an inequality to describe the possible values of x.

15. Which inequality describes the possible values of x?

F x > 6 H x ≮ 12

G x < 6 J 6 < x < 12

CHAPTER 6: QUDRILATERALS

1. Find the sum of the measures of the interior angles for a convex heptagon.

2. The measure of an interior angle of a regular polygon is 140. Find the number of sides in the polygon.

3. Which statement ensures that quadrilateral QRST is a parallelogram?

A ∠Q ≅ ∠S C 𝑄𝑇̅̅ ̅̅ ∥ 𝑅𝑆̅̅̅̅

B 𝑄𝑅̅̅ ̅̅ ≅ 𝑇𝑆̅̅̅̅ and 𝑄𝑅̅̅ ̅̅ ∥ 𝑇𝑆̅̅̅̅ D m∠Q + m∠S = 180

4. For parallelogram JKMH, find m∠JHK, m∠HMK, and the value of x.

5. Determine whether the vertices of quadrilateral DEFG form a parallelogram given D(–3, 5), E(3, 6),

F(–1, 0), and G(6, 1).

6. Prove that quadrilateral PQRS is NOT a parallelogram.

7. For rectangle WXYZ with diagonals 𝑊𝑌̅̅ ̅̅ ̅ and 𝑋𝑍̅̅ ̅̅ , WY = 3d + 4 and XZ = 4d – 1, find the value of d.

8. Rectangle ABCD has vertices A(–3, 0), B(–2, 3), C(4, 1), and D(3, –2). Determine where the diagonals

of the rectangle intersect.

9. If m∠BEC = 9z + 45 in rhombus ABCD, find the value of z.

10. In trapezoid HJLK, M and N are midpoints of the legs. Find KL.

11. What is the value of x?

F 2 H 5.5

G 4 J 7

12. What is m∠T in kite STVW?

F 100 H 95

G 130 J 260

13. JKLM is a kite. Complete each statement.

a. 𝑀𝐽̅̅ ̅̅ ≅ _____

b. 𝑀𝐾̅̅ ̅̅ ̅ ⊥ _____

c. m∠L = m∠ _____