Answers BISD TX-Geometry A-CRTriangle Congruence: SAS

Triangle Classification Theorems Answers

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

27°

36°

54°

72°

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Consider the diagram.

SSS.

ASA.

SAS.

HL.

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 1, negative 1), (2, negative 1), and (negative 1, negative 5). Triangle R S T has points (1, 1), (1, 5), and (4, 1).

The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the x-axis and a translation 2 units to the left.

The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the y-axis and a translation 2 units down.

The figures are not congruent. Point R corresponds to point A, but S corresponds to B and T corresponds to C.

The figures are not congruent. Point R does not correspond with point A.

The proof that ΔRST ≅ ΔVST is shown.Given: ST is the perpendicular bisector of RV.Prove: ΔRST ≅ ΔVST

perpendicular bisector theorem

converse of the perpendicular bisector theorem

Pythagorean theorem

SSS congruence theorem

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

acute, because 62 + 102 < 122

acute, because 6 + 10 > 12

obtuse, because 62 + 102 < 122

obtuse, because 6 + 10 > 12

Triangles W X Z and Y Z X share common side X Z. Angles W X Z and X Z Y are right angles. The lengths of sides W X and Z Y are 21 centimeters.

Yes, they are congruent by SAS.

Yes, they are both right triangles.

No, the triangles share side XZ.

No, there is only one set of congruent sides.

An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?

2 < s < 18

6 < s < 12.8

s 18

s 12.8

Which pair of triangles can be proven congruent by SAS?

Option

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.

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 1, 1), (negative 4, 1) and (negative 1, 5). Triangle L M N has points (1, negative 1), (1, negative 4), and (5, negative 1).

The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.

The figures are congruent because a 180 rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.

The figures are not congruent because point B corresponds with point N and point C corresponds with point M.

The figures are not congruent because there is no rigid transformation or combination of rigid transformations that will map ΔABC onto ΔLMN.

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.

∠RXZ and ∠YXZ

∠PXQ and ∠RXS

∠YZX and ∠UZT

∠WZX and ∠XYZ

Triangles A B C and A B F are congruent. Triangle A B C is reflected across line B A to form triangle A B F.

a rotation about point A

a reflection across the line containing CB

a reflection across the line containing BA

a rotation about point B

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

Which congruence theorem can be used to prove △BDA ≅ △DBC?

SAS

AAS

SSS

Triangles A B C and D E F are shown. Triangle A B C is rotated to the left about point A and then is shifted up and to the right to form triangle D E F.

Translate vertex A to vertex D, and then reflect △ABC across the line containing AC.

Translate vertex B to vertex D, and then rotate △ABC around point B to align the sides and angles.

Translate vertex B to vertex D, and then reflect △ABC across the line containing AC.

Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.

The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

4.0 cm

4.1 cm

5.6 cm

5.7 cm

Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support beam that will connect the ends of the two boards measures 20 feet.

It is an acute triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.

It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.

It is an acute triangle. About 7 feet need to be removed from the 20-foot board to create a right triangle.

It is an obtuse triangle. About 7 feet need to be removed from the 20-foot board to create a right triangle.

Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?

The triangle is a right triangle because 52 + 122 = 132.

The triangle is a right triangle because 5 + 13 > 12.

The triangle is not a right triangle because 52 + 132 > 122.

The triangle is not a right triangle because 5 + 12 > 13.

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest tenth?

41.0 in.

51.2 in.

72.4 in.

81.2 in.

An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.Which best describes the range of possible values for the third side of the triangle?

x 18.9

12.5 < x < 18.9

x 26

6 < x < 26

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Triangle Classification Theorems Answers

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