Triangles Unit Test/Review

A line extends from a side of a triangle. Which new angle is created by extending one side of a triangle? a remote interior angle an adjacent interior angle an exterior angle a complementary angle

c

Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side Line segment B C at point M. What is the length of Line segment M C? 16 mm 24 mm 32 mm 48 mm

a

2 horizontal and parallel lines are intersected by 2 diagonal lines to form a triangle with exterior angles. The top angle of the triangle is (2 x + 10) degrees. The bottom right angle of the triangle is 79 degrees. The exterior angle to the bottom left angle is (6 x + 1) degrees. What is the value of x? x = 2.25 x = 11.25 x = 13 x = 22

d

A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex. A regular pentagon is shown. Lines are drawn from each point to a point in the center to form congruent isosceles triangles. The lengths of all lines are congruent. The total number of degrees of all center angles is 360 degrees. The total number of degrees in the center is 360°. If all five vertex angles meeting at the center are congruent, what is the measure of a base angle of one of the triangles? 54° 72° 108° 144°

a

If triangle RST is an acute triangle, then m∠S must be less than 90°. equal to 90°. equal to 100°. greater than 90° and less than 180°.

a

Consider the triangle. Triangle A B C is shown. Side A B has a length of 15, side B C has a length of 8, side C A has a length of 12. The measures of the angles of the triangle are 32°, 53°, 95°. Based on the side lengths, what are the measures of each angle? m<A = 95°, m<B = 53°, m<C = 32° m<A = 32°, m<B = 53°, m<C = 95° m<A = 43°, m<B = 32°, m<C = 95° m<A = 53°, m<B = 95°, m<C = 32°

b

In the triangles, Line segment B C is-congruent-to line segment R S and Line segment A C is-congruent-to line segment T S. Triangles A B C and T R S are shown. Sides A C and T S are congruent. Sides T B and R S are congruent. If RT is greater than BA, which correctly compares angles C and S? m<C = m<S m<C < m<S m<C > m<S m<C ≥ m<S

b

Which are the possible side lengths of a triangle? 3 cm, 5 cm, 9 cm 4 cm, 8 cm, 10 cm 6 cm, 9 cm, 17 cm 8 cm, 10 cm, 18 cm

b

Consider triangle WXY. Triangle W X Y is shown. The length of side W X is 5, the length of side X Y is 10, and the length of side W Y is 14. Which statement about the angles is true? Angle W is greater than angle Y. Angle Y is the largest angle. Angle X is smaller than angle W. Angle W is the smallest angle.

a

In the triangles, Line segment B C is-congruent-to line segment D E and Line segment A C is-congruent-to line segment F E. Triangles A B C and F D E are shown. The lengths of sides A C and F E are congruent. The lengths of sides B C and D E are congruent. If m Angle C is greater than m Angle E, then Line segment A B is ________ Line segment D F. congruent to longer than shorter than the same length as

b

Triangle XYZ is isosceles. Angle Y measures a°. Triangle X Y Z is shown. The lengths of sides Y X and Z X are congruent. Angle X Y Z is a degrees. What expression represents the measure of angle X? 2a a/2 90-a 80-2a

d

Which type of triangle will always have a perpendicular bisector that is also an angle bisector? right scalene obtuse equilateral

d

The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle? 40° 70° 100° 140°

not a,b

Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle. What is true about triangle XYZ? Select three options. Angle Y is a right angle. The measure of angle Z is 45°. The measure of angle X is 36°. The measure of the vertex angle is 72°. The perpendicular bisector of creates two smaller isosceles triangles.

a,b,e

If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true? m∠A = 15° and m∠C = 35° m∠A + m∠B = 155° m∠A + m∠C = 60° m∠A = 20° and m∠C = 30°

b

Triangle K M L is shown. Line L K extends through point J to form exterior angle J K M. Which angle is an adjacent interior angle to ∠JKM? ∠JKL ∠MKL ∠KLM ∠LMK

b

In the triangles, HG = MP and GK = PN. Triangles H G K and M P N are shown. Side H K has a length of 15 millimeters. Side M N has a length of 11 millimeters. Sides H G and M P are congruent. Sides G K and P N are congruent. Which statement about the sides and angles is true? m<G > m<P m<P > m<G HK = MN HG = PN

a

Triangle A B C is shown with its exterior angles. Line C B extends through point D. Line B C extends to form exterior angle that is 135 degrees. Angle C A B is 75 degrees. What is m∠ABC? m∠ABC = 15° m∠ABC = 45° m∠ABC = 60° m∠ABC = 75°

b

Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54. Based on the diagram, which expresses all possible lengths of segment AB? AB = 25 27 < AB < 81 AB = 85 AB< 27 or AB > 81

b

Triangle JKL is isosceles. The measure of angle J is 72° and the measure of angle K is 36°. Which statement describes angle L? Angle L is a base angle and measures 36°. Angle L is a base angle and measures 72°. Angle L is a vertex angle and measures 36°. Angle L is a vertex angle and measures 72°.

b

Lee is creating a garden with the dimensions shown. Lines are drawn inside a large triangle at each point to create smaller triangles. Line A B is drawn to create a triangle that has 2 sides with a length of 8 feet. The angle opposite to A B is 36 degrees. Line Z Y is drawn to create a triangle that has 2 sides with a length of 8 feet. The angle opposite to Z Y is 65 degrees. Line X Y is drawn to create a triangle that has 2 sides with a length of 8 feet. The angle opposite to X Y is 79 degrees. He creates paths through the garden along Line segment A B, Line segment X Y, and Line segment Z Y. Which correctly compares the lengths of the paths? The path along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B. The path along Line segment A B is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment X Y. The path along Line segment Z Y is longer than the path along Line segment X Y, and the path along Line segment X Y is longer than the path along Line segment A B. The path along Line segment Z Y is longer than the path along Line segment A B, and the path along Line segment A B is longer than the path along Line segment X Y.

a

Lines P S and W T are horizontal and parallel. Lines V R and Q R are diagonal and intersect lines P S and W T to form triangle X Y Z. Which pair of angles is supplementary? ∠RXZ and ∠YXZ ∠PXQ and ∠RXS ∠YZX and ∠UZT ∠WZX and ∠XYZ

a

Triangle ABC has the angle measures shown. m<A=(2x)° m<b=(5x)° m<c=(11x)° Which statement is true about the angles? m<A=20° m<b=60° <A and <B are complementary m<A+m<c=120°

a

Triangle KNM is shown. Angle M K N is 25 degrees. Angle K N M is 130 degrees. Angle N M K is 25 degrees. What is true about the sides of KNM? KN = NM KN + NM = KM KM = 2(NM) KN = 1/2 KM

a

A triangle with exterior angles is shown. The bottom right angle of the triangle is (3 h + 18) degrees. The bottom right exterior angle is (15 h) degrees. What is the value of h? h = 1.5 h = 9 h = 10 h = 13.5

b

Choose the word that correctly completes the statement. Triangle A B C is shown. Angle A C B is 45 degrees, angle C B A is 75 degrees, and angle B A C is 60 degrees. Since angle B is the largest angle, Line segment A C is the ________ side. adjacent included longest shortest

c

In the triangles, XY = MP and YZ = PN. Triangles Y X Z and P M N are shown. The length of side X Z is 23 inches. The length of side M N is 19 inches. Sides X Y and M P are congruent. Sides Y Z and P N are congruent. If m<P = 85°, which is a possible measure for <Y? m<Y = 80° m<Y = 85° m<Y = 100° m<Y = 180°

c

A triangle has a bottom left angle of (x + 15) degrees and a bottom right angle of (x degrees). 1 parallel and horizontal line sits at the top point of the triangle. Another parallel and horizontal line sits at the base of the triangle. The exterior angle to the bottom right angle of the triangle is (4 x minus 20) degrees. What is the value of x? x = 32 x = 36 x = 37 x = 40

d

Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides of this triangle? 5 cm and 8 cm 6 cm and 7 cm 7 cm and 2 cm 8 cm and 8 cm

d

In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS? QS = 13 5 < QS < 8 QS > 13 3 < QS < 13

d

Steven is cutting an 11 ft piece of lumber into three pieces to build a triangular garden. Which diagram shows a way in which he can cut the wood to create three pieces that can form a triangle? A piece of wood is cut into 3 pieces. The pieces are: 2 feet, 2 feet, and 7 feet. A piece of wood is cut into 3 pieces. The pieces are: 1 foot, 4 feet, 6 feet. A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 2 feet, and 6 feet. A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 4 feet, 4 feet.

d

Nigel and Mia are searching for a treasure chest under water. The straight line distance between them is 100 meters. A triangle has points Nigel, Mia, and Treasure Chest. The distance from Nigel to Mia is 100 meters. The angle between Treasure Chest, Nigel, and Mia is 65 degrees. The angle between Nigel, Mia, and Treasure Chest is 80 degrees. Given the angles in the diagram, who is closer to the treasure chest and why? Nigel is closer because his distance to the chest is opposite the larger angle. Mia is closer because her distance to the chest is opposite the smaller angle. Nigel is closer because his distance from the chest is 100 meters. Mia is closer because her distance from the chest is 100 meters.

b

The lengths of the sides of triangle XYZ are written in terms of the variable m, where m ≥ 6. Triangle X Y Z is shown. The length of side X Y is m + 8, the length of side Y Z is 2 m + 3, the length of side Z X is m minus 3. Which is correct regarding the angles of the triangle? m<X < m<Z < m<Y m<Y < m<Z < m<X m<Y < m<X < m<Z m<Z < m<Y < m<X

b

Triangle T U V is shown. Side T U has a length of 5 units, side U V has a length of 8 units, and side T V has a length of 11 units. Which statement is true regarding triangle TUV? Angle T is the smallest angle. Angle V is the smallest angle. Angles U and V must be equal. Angles U and T must be equal.

b

Which diagram shows possible angle measures of a triangle? A triangle has angle lengths 35 degrees, 115 degrees, and 25 degrees. A triangle has angle lengths 32 degrees, 115 degrees, and 33 degrees. A triangle has angle lengths 35 degrees, 120 degrees, and 35 degrees. A triangle has angle lengths 30 degrees, 120 degrees, and 20 degrees.

b

Consider triangle WXY. Triangle W X Y is shown. The length of side W X is 5% 2 Triangle E B C is shown with its exterior angles. Line E C extends through point F. Line C B extends through point A. Line B E extends through point D. Which statements regarding the diagram of ΔEBC are true? Select three options. ∠BEC is an exterior angle. ∠DEC is an exterior angle. ∠ABE and ∠EBC are supplementary angles. ∠BCF and ∠DEC are supplementary angles. ∠BEC is a remote interior angle to exterior ∠BCF.

b,c,d

The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle? 27° 36° 54° 72°

d

Triangle B C D is shown. Line D B extends through point A to form exterior angle A B C. Angle B D C is 67 degrees and Angle C D B is 60 degrees. What is m∠ABC? m∠ABC = 60° m∠ABC = 67° m∠ABC = 120° m∠ABC = 127°

d

Triangle DEF is isosceles, where Line segment D F is-congruent-to line segment F E. Angle FDE is bisected by segment DG, creating angle GDE with a measure of 29°. Isosceles triangle D E F is shown. Angle F D E is bisected by segment D G. Angle G D E is 29 degrees. What is the measure of angle DFE? 29° 32° 58° 64°

d