Answers GRADY 24-25 VA-GeometryTriangle Congruence: SAS

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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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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.

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.

h = 1.5

h = 9

h = 10

h = 13.5

Consider the diagram.

SSS.

ASA.

SAS.

HL.

Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent.

Yes, but only if AB ≅ DC.

Yes, but only if BC ≅ DC.

No, because AB is not congruent to AC.

No, because AB ≅ DA.

A line extends from a side of a triangle.

a remote interior angle

an adjacent interior angle

an exterior angle

a complementary angle

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

right

scalene

obtuse

equilateral

Which pair of triangles can be proven congruent by the HL theorem?

2 right triangles have congruent hypotenuses.

2 triangles have one congruent angle and 2 congruent sides.

2 right triangles have congruent hypotenuses and another congruent side.

2 triangles have 3 congruent sides.

A triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft.

x – 1 < n < 3x + 5

n = 3x + 5

n = x – 1

3x + 5 < n < x – 1

Triangles D E F and D prime E prime F prime are connected at point E. Triangle D E F is rotated about point E to form triangle D prime E prime F prime.

dilation

reflection

rotation

translation

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.

A line extends from a side of a triangle.

a remote interior angle

an adjacent interior angle

an exterior angle

a complementary angle

[Figure may not be drawn to scale]

25 units

50 units

100 units

150 units

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.

m∠ABC = 60°

m∠ABC = 67°

m∠ABC = 120°

m∠ABC = 127°

Which pair of triangles can be proven congruent by SAS?

Option

Which pair of triangles can be proven congruent by the HL theorem?

2 right triangles have congruent hypotenuses.

2 triangles have one congruent angle and 2 congruent sides.

2 right triangles have congruent hypotenuses and another congruent side.

2 triangles have 3 congruent sides.

Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.

A ≅ Q because of the third angle theorem.

AB ≅ QN because they are both opposite a right angle.

BC ≅ NM because it is given.

C ≅ M because right angles are congruent.

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

is the angle bisector of YEX and the perpendicular bisector of . is the angle bisector of YGZ and the perpendicular bisector of . is the angle bisector of ZFX and the perpendicular bisector of . Point A is the intersection of , , and .

Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.

Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.

Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.

Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z.

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.

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 3, negative 1), (negative 1, 2), and (negative 5, 3). Triangle R S T has points (1, 1), (3, 4), and (5, 0).

ΔRST ≅ ΔACB

ΔRST ≅ ΔABC

ΔRST ≅ ΔBCA

ΔRST ≅ ΔBAC

Triangle DEF is isosceles, where . Angle FDE is bisected by segment DG, creating angle GDE with a measure of 29°.

29°

32°

58°

64°

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.

The proof that UX ≅ SV is shown.Given: △STU an equilateral triangle∠TXU ≅ ∠TVSProve: UX ≅ SVWhat is the missing statement in the proof?StatementReason1. ∠TXU ≅ ∠TVS1. given2. ∠STV ≅ ∠UTX2. reflex. prop.3. △STU is an equilateral triangle3. given4. ST ≅ UT4. sides of an equilat. △ are ≅5. ?5. AAS6. UX ≅ SV6. CPCTC

△SXU ≅ △TVS

△UVX ≅ △SXV

△SWX ≅ △UWV

△TUX ≅ △TSV

A triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft.

x – 1 < n < 3x + 5

n = 3x + 5

n = x – 1

3x + 5 < n < x – 1

Triangle ABC has the angle measures shown.

Measure of angle A = 20 degrees

Measure of angle B = 60 degrees

are complementary

Measure of angle A + measure of angle C = 120 degrees

Triangles A B C and E D C are shown. Triangle A B C is rotated about point C to form triangle E D C.

a rotation about point B

a reflection across the line containing CB

a reflection across the line containing AC

a rotation about point C

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 theorems can be used to prove ΔABR ≅ ΔACR? Select three options.HLSASSSSASAAAS

SAS

SSS

ASA

AAS

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.

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

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

SAS

AAS

SSS

Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side at point M.What is the length of ?

16 mm

24 mm

32 mm

48 mm

Triangle ABC is rotated 45° about point X, resulting in triangle EFD.

3.3 cm

3.6 cm

4.2 cm

4.5 cm

How can ΔABC be mapped to ΔXYZ?

vertex B to vertex Z

vertex B to vertex Y

vertex A to vertex Z

vertex A to vertex Y

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