Introduction: Geometry Honors Final Exam Practice

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This is a practice Geometry Honors Final Exam with clues and answers. I hope it's useful!

Step 1: Which Is the Distance Between Points (-3, 4) and (2, 5)?

  1. 5
  2. 24
  3. √24
  4. √26
  5. 26

d=√((x_2-x_1)²+(y_2-y_1)²)

Answer: 4) √26

Step 2: Conditions

Let p represent "I live in Virginia" and q represent "I am an senior". Which is the symbolic notation for "I live in Virginal and I am not a senior"

  1. p∧∼q
  2. p∨∼q
  3. p→∼q
  4. p⟷∼q

and = ∧

Answer: 1) p∧∼q

Step 3: Triangle Angle Proofs

What additional piece of information would prove △LMK≅△NMK by side-angle-side?

  1. ∠MLK≅∠MNK
  2. MK (line segment) bisects ∠LKN
  3. ∠LMK≅∠NMK
  4. M is the midpoint of LN (line segment)

Line segments LK and NK are equal and both triangles share the same line segment MK.

In one step, only angles ∠MKL and ∠MKN have to be congruent.

Bisecting means splitting something in to equal halves.

Therefore, line segment MK should bisect ∠LKN in order for both triangles to be congruent by side-angle-side.

Answer: 2) MK (line segment) bisects ∠LKN

Step 4: Which Is Closest to the Area of the Shaded Sector of Circle C?

  1. 38 cm^2
  2. 45 cm^2
  3. 34 cm^2
  4. 29 cm^2

Answer: 4) 29cm^2

Step 5: Similar Triangles

Based on the given information, which diagram contains a pair of similar triangles?

Answer: Image 3

The sum to all angles of any triangle is 180 degrees

64+25+X=180

X=91

Therefore, the triangles are similar.

Step 6: Area of a Hexagon

What is the area of a regular hexagon with apothem length of 9?

  1. 162√3
  2. 486√3
  3. 162√2
  4. 4862√

A=(3√3)/2 a^2

a= side

Answer: 1) 162√3



Step 7: Volume of a Sphere

Mikayla is filling a glass sphere with water. If the diameter of the sphere is 12 inches, what is the minimum amount of water she needs to completely fill the sphere?

  1. 288π in^3
  2. 2,304π in^3
  3. 144π in^3
  4. 576π in^3

V = 4/3 π r³

diameter = 2r

Answer: 1) 288π in^3

Step 8: What Is the Midpoint of the Segment With Endpoints (-6, 3) and (3, 6)?

  1. (-4.5, -1.5)
  2. (-1.5, 4.5)
  3. (0, -2)
  4. (12, 9)

midpoint formula: ((x1 + x2)/2, (y1 + y2)/2)

Answer: 2) (-1.5, 4.5)

Step 9: Hexagons

If each interior angle of a regular hexagon measures (13x+3)°, which is the value of x?

  1. 11
  2. 9
  3. 10
  4. 12

Answer: 9

Step 10: True or False

Three points are always coplanar. = True

If two angles are supplementary, then they form a linear pair. = False

If the sides of a triangle are 2√6, 3√2, √6, then it is a 30-60-90 triangle. = True

The converse of p → q is q → p = True

AA is a way to prove two triangles are congruent. = False

The interior angles of a pentagon sum to 900 degrees. = False

The center of circle (x−9)^2 +(y+2)^2=81 is (-9, 2). = False

The diagonals of a rhombus are always congruent. = False

The sum of the lengths of two sides of a triangle is always greater than the length of the third side. = True

Opposite rays form a line. = True

Step 11: What Value of X Would Prove A∥b?

  1. 8
  2. 11
  3. 10
  4. 9

Answer: 1) 8

Step 12: Equilateral Triangle

If △ABC is an equilateral triangle and BD = 36 inches, find the value of x.

  1. 18√3
  2. 12√3
  3. 24√3
  4. 36√3

Answer: 3) 24√3

Step 13: Finding Angles

  1. 66°
  2. 52°
  3. 34°
  4. 38°

Answer: 4) 38

Step 14: Always, Sometimes, Never

If AM = MB, then M is the midpoint of AB = Sometimes

Alternate interior angles are congruent. = Sometimes

An equilateral triangle is isosceles. = Always

The diagonals of a rhombus are perpendicular. = Always

Two right triangles with congruent hypotenuses are congruent triangles. = Sometimes

The contrapositive of a true conditional statement is false. = Never

An isosceles triangle has a right angle. = Sometimes

Vertical angles are congruent. = Always

The lateral area of a solid includes the area of the solid's bases. = Never

Three points determine a plane. = Sometimes


Step 15: Distance

An 85 foot wire is tied from the top of a utility pole to the top of a building as shown. Find d, the distance from the pole to the building. Make sure you are in degree mode!

  1. 75.2 ft
  2. 78.8 ft
  3. 80.5 ft
  4. 82.1 ft

Answer: 2) 78.8 ft

Step 16: Given Circle S, Find M∠TUV ?

  1. 28 degrees
  2. 32 degrees
  3. 58 degrees
  4. 36 degrees

Answer: 2) 32 degrees

Step 17: Triangle Angles

Park Street, Scott Street, and Oak Street form a triangle. If the angle formed by Oak Street and Park Street is 62°

62° and the angle formed by Park Street and Scott Street is 58°

58°, list the sides of the triangle from least to greatest.


Answer: 1) Oak Street

2) Park Street

3) Scott Street

Step 18: Which Line Represents a Line Parallel to Y=-2x + 9?

  1. 4x-2y=10
  2. 2x-4y=28
  3. 2x+4y=28
  4. 4x+2y=10

Parallel lines have the same slope.

Answer: 4) 4x+2y=10

Step 19: Surface Area

The volume of Prism A is 1,536 m^3 and the volume of Prism B is 375 m^3. What is the ratio of their surface area?

  1. 512:125
  2. 64:25
  3. 8:5
  4. 16:25

Answer: 2) 64:25

Step 20: Which Angle Measure Is Closest to the Value of X?

Make Sure You Are In Degree Mode!

  1. 39.8 degrees
  2. 50.1 degrees
  3. 56.4 degrees
  4. 33.6 degrees

Answer: 4) 33.6 degrees

Step 21: Right Triangles

Given the side measures, which of the following could form a right triangle?

  1. 55 ft, 45 ft, 35 ft
  2. 24 in, 34 in, 28 in
  3. 61 m, 60 m, 11 m
  4. 48 cm, 46 cm, 15 cm

Answer: 3) 61 m, 60 m, 11 m

Step 22: If QRST Is an Isosceles Trapezoid, Find the M∠R.

  1. 118 degrees
  2. 125 degrees
  3. 107 degrees
  4. 113 degrees

Answer: 4) 113 degrees