Answers GRADY 24-25 VA-GeometryTriangle Congruence: SAS

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Which congruence theorem can be used to prove △WXS ≅ △YZS?

SSS

ASA

SAS

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Three quadrilaterals exist such that GHJK ≅ ASDF and GHJK ≅ VBNM.If MV measures 3 cm, which other segment must measure 3 cm?

Which pair of triangles can be proven congruent by SAS?

2 identical triangles are shown. The triangle is reflected across a line to form the second triangle.

2 identical triangles are shown. The triangle is rotated 90 degrees to form the second triangle.

2 identical triangles are shown. The triangle is reflected across a line and then rotated to form the second triangle.

2 identical triangles are shown. The triangle is rotated up and to the left 90 degrees to form the second triangle.

The triangles are congruent by the SSS congruence theorem.

reflection only

rotation only

translation, then reflection

translation, then rotation

Triangle KNM is shown.

KN = NM

KN + NM = KM

KM = 2(NM)

KN = KM

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.

m∠ABC = 15°

m∠ABC = 45°

m∠ABC = 60°

m∠ABC = 75°

In ΔXYZ, m∠X = 90° and m∠Y = 30°. In ΔTUV, m∠U = 30° and m∠V = 60°. Which is true about the two triangles?

ΔXYZ ≅ ΔTUV

ΔXYZ ≅ ΔVUT

No congruency statement can be made because only two angles in each triangle are known.

No congruency statement can be made because the side lengths are unknown.

The proof that ΔQPT ≅ ΔQRT is shown.Given: SP ≅ SRProve: ΔQPT ≅ ΔQRT

definition of perpendicular bisector

definition of congruence

reflexive property

substitution property

Triangle L N P has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, L P, and Q M. The length of line segment N S is 7 x minus 3 and the length of line segment S R is 5 x minus 3.

1 unit

2 units

4 units

6 units

Triangles Q R S and A B C are shown. The lengths of sides Q R and A B are 16 centimeters. The lengths of sides R S and B C are 24 centimeters. Angles Q R S and A B C are right angles. Sides Q S and A C are parallel and identical to each other and there is space in between the 2 triangles.

No, ΔQRS and ΔABC are congruent but ΔQRS cannot be mapped to ΔABC using a series rigid transformations.

No, ΔQRS and ΔABC are not congruent.

Yes, ΔQRS can be translated so that R is mapped to B and then rotated so that S is mapped to C.

Yes, ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.

Triangles D E F and G H J are congruent. Triangle D E F is shifted down and to the right to form triangle G H J.

dilation

reflection

rotation

translation

Triangle T R S has centroid Z. Lines are drawn from each point to the midpoint of the opposite side to form line segments T W, R V, and S U.

3 inches

6 inches

12 inches

18 inches

Triangles J K L and M N R are shown.

KL ≅ NR

∠L ≅ ∠R

∠K ≅ ∠N

JK ≅ MN

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°.

Point Z is the incenter of ΔSRT.

24°

31°

35°

62°

A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex.

54°

72°

108°

144°

Triangle XYZ is isosceles. Angle Y measures a°.

StartFraction a Over 2 EndFraction

90 a

180 2a

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°.

Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?

AAS

SSS

SAS

Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.

AB = 25

27 < AB < 81

AB = 85

AB< 27 or AB > 81

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.

Point X is the circumcenter of ΔABC.What is the length of XB?

4.2 cm

4.6 cm

4.8 cm

5.3 cm

The proof that MNG ≅ KJG is shown.Given: N and J are right angles; NG ≅ JGProve: MNG ≅ KJG

the reflexive property

ASA

AAS

the third angle theorem

Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent.

LO ≅ LM

OA ≅ MA

LOA ≅ LMA

LAO ≅ LAM

Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.

Yes, they are congruent by either ASA or AAS.

Yes, they are both right triangles.

No, M is not congruent to NLQ.

No, there are no congruent sides.

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.

x = 2.25

x = 11.25

x = 13

x = 22

Quadrilateral ABCD is translated down and left to form quadrilateral OLMN.

5 units

6 units

8 units

10 units

Triangles A B C and Q R S are shown. Sides A B and Q R are congruent. Angles C A B and R Q S are congruent. Angles Q S R and A C B are congruent.

a reflection across the line containing AB

a rotation about point B

a reflection across the line containing CB

a rotation about point C

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 9 cm

The proof that HG ≅ EG is shown.Given: G is the midpoint of KFKH ∥ EFProve: HG ≅ EGWhat is the missing reason in the proof?StatementReason1. ∠EGF ≅ ∠HGK1. vert. ∠s are ≅2. KH ∥ EF2. given3. ∠F ≅ ∠K3. alt. int. ∠s are ≅4. G is the midpoint of KF4. given5. FG ≅ KG5. def. of midpt.6. △FEG ≅ △KHG6. ?7. HG ≅ EG7. CPCTC

SAS

ASA

AAS

Quadrilateral L M N O is reflected over a line to form quadrilateral C D A B.

Triangle K M L is shown. Line L K extends through point J to form exterior angle J K M.

∠JKL

∠MKL

∠KLM

∠LMK

Given: bisects ∠MRQ; ∠RMS ≅ ∠RQS

ΔMNR ≅ ΔMNS by ASA

ΔRMS ≅ ΔRQS by AAS

ΔSNQ ≅ ΔSNM by SSS

ΔQNR ≅ ΔMNR by HL

Triangles H J K and L M N are shown. The triangles have identical side lengths and angle measures. Triangle H J K is slightly lower and to the left of triangle L M N. Triangle H J K is reflected to form triangle L M N.

Translate K to N and reflect across the line containing HJ.

Translate K to N and reflect across the line containing JK.

Translate H to L and reflect across the line containing JK.

Translate K to L and reflect across the line containing HJ.

Triangles J K L and X Y Z are shown. Angles K J L and Y X Z are right angles. The length of Y X is 10. The length of hypotenuse K L is 10.

Yes, if JL ≅ XZ.

Yes, if XZ = 10.

No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.

No, because the leg of one triangle is equal in length to the leg of the other triangle.

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°

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