TCAP Geometry End-of-Course Assessment

Point P(3, -4) is translated using the vector <-5, 2>. What are the coordinates of the image P'?

• A(-2, -2)
• B(8, -6)
• C(-2, 2)
• D(2, -6)

Point A(-4, 7) is reflected across the y-axis. What are the coordinates of image A'?

• A(-4, -7)
• B(4, 7)
• C(4, -7)
• D(7, -4)

Point B(2, -5) is rotated 180 degrees counterclockwise about the origin. What are the coordinates of B'?

• A(-5, 2)
• B(5, -2)
• C(-2, 5)
• D(2, 5)

Triangle ABC has side lengths AB = 6, BC = 8, and AC = 10. If triangle ABC is congruent to triangle DEF, what is the length of segment EF?

• A6
• B10
• C14
• D8

In triangle PQR, PQ = PR. If the measure of angle P is 40 degrees, what is the measure of angle Q?

• A70°
• B40°
• C100°
• D140°

Two parallel lines are cut by a transversal. If one angle measures 65 degrees, what is the measure of its consecutive interior angle?

• A65°
• B115°
• C125°
• D180°

Which triangle congruence postulate or theorem can be used to prove two right triangles are congruent if their hypotenuses and one pair of legs are congruent?

• ASide-Angle-Side (SAS)
• BAngle-Side-Angle (ASA)
• CHypotenuse-Leg (HL)
• DSide-Side-Side (SSS)

When constructing the perpendicular bisector of segment AB using a compass and straightedge, what must be true about the compass width setting?

• AIt must be equal to the length of segment AB.
• BIt must be less than half the length of segment AB.
• CIt can be any width regardless of segment length.
• DIt must be greater than half the length of segment AB.

Point M(3, 4) is rotated 90 degrees counterclockwise about the origin, and then translated by vector <2, -1>. What are the coordinates of the final image M''?

• A(-2, 2)
• B(-4, 3)
• C(6, 3)
• D(2, -2)

Lines l and m are parallel. Line t is a transversal. Angle 1 and Angle 2 are alternate exterior angles. If m∠1 = (3x + 15)° and m∠2 = (5x - 25)°, what is the value of x?

• A15
• B20
• C25
• D30

In triangle ABC, m∠A = (2x + 5)°, m∠B = (x + 15)°, and the exterior angle at vertex C measures (4x - 10)°. What is the measure of interior angle C?

• A60°
• B110°
• C70°
• D50°

Triangles ABC and DEF are given. AB = DE = 8 cm, BC = EF = 12 cm, and m∠B = m∠E = 50 degrees. Which theorem proves triangle ABC is congruent to triangle DEF?

• ASSS Postulate
• BASA Postulate
• CAAS Theorem
• DSAS Postulate

Segment AB has endpoints A(-2, 3) and B(6, -1). What is the equation of the perpendicular bisector of segment AB?

• Ay = 2x - 3
• By = -2x + 5
• Cy = 0.5x
• Dy = 2x + 1

Quadrilateral ABCD is a parallelogram with m∠A = (5x - 12)° and m∠C = (3x + 24)°. What is the measure of angle B?

• A78°
• B102°
• C18°
• D90°

In quadrilateral XYZW, diagonals XZ and YW bisect each other at right angles and are congruent. What specific type of polygon must XYZW be?

• ARhombus
• BRectangle
• CSquare
• DTrapezoid

Triangle JKL has vertex K(4, 6). If the triangle is reflected across the line y = x, what are the coordinates of K'?

• A(-4, -6)
• B(4, -6)
• C(-6, 4)
• D(6, 4)

In a formal proof, statement 4 reads: '∠1 ≅ ∠2'. If ∠1 and ∠2 form a linear pair of congruent angles, which reason justifies that each angle measures 90 degrees?

• AIf two angles are both supplementary and congruent, then each is a right angle.
• BVertical Angles Theorem
• CAlternate Interior Angles Theorem
• DDefinition of complementary angles

In rhombus RHOM, diagonals RO and HM intersect at E. If RE = 6 cm and HE = 8 cm, what is the perimeter of rhombus RHOM?

• A28 cm
• B40 cm
• C48 cm
• D20 cm

A student performs a geometric construction to bisect angle ABC. Which compass and straightedge steps guarantee that point D lies on the angle bisector?

• ADrawing a line perpendicular to segment AB through C
• BFinding the midpoint of segment AC with a ruler
• CConstructing equal-radius arcs centered at points on rays BA and BC that intersect at D
• DMeasuring angle ABC with a protractor and dividing by 2

In isosceles trapezoid ABCD with AB || CD, m∠A = (4x + 20)° and m∠D = (2x + 40)°. What is the measure of angle B?

• A20°
• B60°
• C80°
• D100°

Triangle ABC has vertex B(2, 5). Triangle A'B'C' is formed by reflecting triangle ABC over the line y = 1 and then rotating it 90 degrees counterclockwise about the origin. What are the coordinates of B''?

• A(3, 2)
• B(-3, 2)
• C(3, -2)
• D(2, 3)

In triangle ABC, D is on AB and E is on AC such that DE || BC. If AD = 2x + 1, DB = 3x - 1, AE = 6, and EC = 8, what is the length of segment AB?

• A28
• B35
• C20
• D15

In a coordinate proof proving that the diagonals of a rectangle are congruent, rectangle OABC has vertices O(0, 0), A(a, 0), B(a, b), and C(0, b). What are the lengths of diagonals OB and AC?

• AOB = a + b, AC = a - b
• BOB = sqrt(a^2 - b^2), AC = sqrt(a^2 - b^2)
• COB = sqrt(a^2 + b^2), AC = sqrt(a^2 + b^2)
• DOB = a^2 + b^2, AC = a^2 + b^2

In triangle ABC, the altitude from A intersects BC at D. If AB = 13, AC = 15, and AD = 12, what is the length of side BC if D lies between B and C?

• A9
• B12
• C5
• D14

An exterior angle of a regular polygon measures 24 degrees. How many sides does this regular polygon have?

• A15
• B12
• C18
• D20

Point P(4, -6) is dilated by a scale factor of k = 1.5 with the center of dilation at the origin. What are the coordinates of P'?

• A(4, -9)
• B(6, -9)
• C(6, -6)
• D(2.67, -4)

Two triangles are similar with a scale factor of 3:5. If the smaller triangle has a perimeter of 24 cm, what is the perimeter of the larger triangle?

• A30 cm
• B36 cm
• C40 cm
• D60 cm

A right triangle has legs of length 9 cm and 12 cm. What is the length of the hypotenuse?

• A13 cm
• B21 cm
• C14 cm
• D15 cm

In a 45-45-90 right triangle, each leg has a length of 7 cm. What is the exact length of the hypotenuse?

• A7√2 cm
• B14 cm
• C7√3 cm
• D3.5√2 cm

In a 30-60-90 right triangle, the side opposite the 30-degree angle measures 5 cm. What is the length of the hypotenuse?

• A5√3 cm
• B10 cm
• C10√3 cm
• D2.5 cm

In right triangle ABC with ∠C = 90 degrees, side AC = 8 and hypotenuse AB = 17. What is the value of cos(A)?

• A15/17
• B8/15
• C8/17
• D17/8

If sin(34°) = cos(x), where x is an acute angle in degrees, what is the value of x?

• A34°
• B146°
• C68°
• D56°

Triangle ABC is similar to triangle DEF. If m∠A = 42 degrees and m∠B = 68 degrees, what is m∠F?

• A70°
• B42°
• C68°
• D110°

In right triangle ABC, altitude CD is drawn to hypotenuse AB. If AD = 4 cm and DB = 16 cm, what is the length of altitude CD?

• A64 cm
• B8 cm
• C10 cm
• D4√5 cm

In right triangle ABC, altitude CD is drawn to hypotenuse AB. If AD = 3 cm and DB = 9 cm, what is the length of leg AC?

• A3√3 cm
• B6 cm
• C6√3 cm
• D12 cm

A ladder leaning against a wall makes a 60-degree angle with the ground. If the base of the ladder is 8 feet away from the wall, how high up the wall does the ladder reach?

• A16 feet
• B8 feet
• C4√3 feet
• D8√3 feet

Two similar cylinders have surface areas of 36π cm² and 100π cm². If the volume of the smaller cylinder is 54π cm³, what is the volume of the larger cylinder?

• A250π cm³
• B150π cm³
• C450π cm³
• D180π cm³

A building casts a shadow 45 meters long. At the same time, a 2-meter tall post casts a shadow 3 meters long. How tall is the building?

• A22.5 meters
• B30 meters
• C67.5 meters
• D40 meters

In triangle ABC, side a = 7, side b = 9, and included angle C = 30 degrees. What is the area of triangle ABC?

• A31.5
• B63
• C15.75
• D27

In non-right triangle ABC, side a = 10 cm, m∠A = 30 degrees, and m∠B = 45 degrees. What is the length of side b?

• A5 cm
• B10 cm
• C5√2 cm
• D10√2 cm

In triangle ABC, side a = 5, side b = 8, and side c = 7. What is the measure of angle C?

• A60°
• B45°
• C90°
• D120°

A surveyor measures the angle of elevation to the top of a tower as 35 degrees from a distance of 120 feet along flat ground. Which expression gives the height of the tower in feet?

• A120 / tan(35°)
• B120 * tan(35°)
• C120 * sin(35°)
• D120 / cos(35°)

Point A(1, 2) is dilated with scale factor k = 3 centered at point C(3, 4). What are the coordinates of image A'?

• A(3, 6)
• B(-5, -6)
• C(-3, -2)
• D(-1, 0)

In right triangle XYZ with m∠Y = 90 degrees, tan(X) = 3/4. What is the value of sin(Z)?

• A3/5
• B3/4
• C5/4
• D4/5

Triangle ABC has side lengths AB = 12, BC = 16, and AC = 20. Triangle DEF has side lengths DE = 18, EF = 24, and DF = 30. Which similarity theorem proves triangle ABC is similar to triangle DEF?

• ASSS Similarity Theorem
• BSAS Similarity Theorem
• CAA Similarity Postulate
• DHL Similarity Theorem

An observer on top of a 150-foot cliff spots a boat at an angle of depression of 22 degrees. To the nearest foot, how far is the boat from the base of the cliff?

• A402 feet
• B371 feet
• C340 feet
• D162 feet

In triangle ABC, m∠A = 30 degrees, m∠C = 45 degrees, and side c = 6√2 cm. What is the exact length of side a?

• A12 cm
• B3√2 cm
• C6 cm
• D6√2 cm

In right triangle ABC with hypotenuse AB = 25, altitude CD to hypotenuse AB divides AB into segments AD and DB. If AC = 15, what is the length of DB?

• A9
• B12
• C20
• D16