Triangle Congruence: ASA and AAS

Which shows two triangles that are congruent by AAS? 2 right triangles are connected at one side. The triangles have 1 congruent side and 2 congruent angles. The second triangle is a reflection of the first triangle. 2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated to form the second triangle. 2 triangles are connected at one side. All sides are congruent. 2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated and then translated down to form the second triangle.

A

Triangles A B C and T P Q are shown. Sides A C and T Q are congruent. Angles B C A and P Q T are congruent. Which statements are true about additional information for proving that the triangles are congruent? Select two options. If AngleA ≅ AngleT, then the triangles would be congruent by ASA. If AngleB ≅ AngleP, then the triangles would be congruent by AAS. If all the angles are acute, then the triangles would be congruent. If AngleC and AngleQ are right angles, then triangles would be congruent. If BC ≅ PQ, then the triangles would be congruent by ASA.

A,B

The proof ▵ABC ≅ ▵DCB that is shown. Given: <A ≅ <D; CD||AB Prove: ▵ABC ≅ ▵DCB Triangles C D B and C A B are shown. Angles C D B and C A B are congruent. Sides D C and A B are parallel. What is the missing reason in the proof? A 2-column table has 5 rows. Column 1 is labeled Statement with entries angle A is-congruent-to angle D, line segment C D is parallel to line segment A B, line segment C B is-congruent-to line segment B C, angle A B C is-congruent-to angle D C B, triangle A B C is-congruent-to triangle D C B. Column 2 is labeled Reason with entries given, given, reflective property, alternating interior angles are congruent, question mark. alt. ext. <s are ≅ ASA AAS corr. int. <s are ≅

C

Triangle J K L is rotated slightly about point L to form triangle M N Q. Two rigid transformations are used to map TriangleJKL to TriangleMNQ. The first is a translation of vertex L to vertex Q. What is the second transformation? a reflection across the line containing LK a reflection across the line containing JK a rotation about point L a rotation about point K

C

Triangles L K N and P Q M are shown. Sides K L and Q P are congruent. Angles L K N and P Q M are right angles. What additional information is needed to prove that the triangles are congruent using the ASA congruence theorem? NL ≅ MP NK ≅ MQ <N ≅ <M <L ≅ <P

D

Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?

D

Given: Angle A B C and Angle F G H are right angles; Line segment B A is parallel to line segment G F; Line segment B C is-congruent-to line segment G H Prove: Triangle A B C Is-congruent-to Triangle F G H Triangles A B C and F G H are shown. Triangle F G H is slightly lower and to the left of triangle A B C. Lines extend from sides B A and G F to form parallel lines. Another line connects points F and C. Angles A B C and F G H are right angles. Sides B C and G H are congruent. Step 1: We know that Angle A B C Is-congruent-to Angle F G H because all right angles are congruent. Step 2: We know that Angle B A C Is-congruent-to Angle G F H because corresponding angles of parallel lines are congruent. Step 3: We know that Line segment B C is-congruent-to line segment G H because it is given. Step 4: Triangle A B C Is-congruent-to Triangle F G H because of the ASA congruence theorem. AAS congruence theorem. third angle theorem. reflexive property.

B

Which shows two triangles that are congruent by ASA? 2 right triangles are connected at one side. The triangles have 2 congruent sides and one congruent angle. 2 triangles are connected at one side. The triangles also have 2 congruent angles. The first triangle can be rotated to form the second triangle. 2 triangles have 3 congruent angles. The second triangle is to the right of the first triangle. 2 triangles have 2 congruent sides and 1 congruent angles. The first triangle is reflected across a line and then rotated to form the second triangle.

B

Triangles A B C and R M Q are shown. Angles C A B and M R Q are 29 degrees. Angles A B C and R M Q are 116 degrees. What additional information could be used to prove that the triangles are congruent using AAS? Select two options. AngleC ≅ AngleQ CB ≅ QM AC = 3.9cm and RQ = 3.9cm mAngleC = 35° and mAngleQ = 35° AB = 2.5cm and MQ = 2.5cm

B,C

Triangles A B C and T P Q are shown. Angles B C A and P Q T are congruent. What additional information could be used to prove that the triangles are congruent using AAS or ASA? Select three options. <B ≅ <P and BC ≅ PQ <A ≅ <T and AC = TQ = 3.2cm <A ≅ <T and <B ≅ <P <A ≅ <T and BC ≅ PQ AC = TQ = 3.2 cm and CB = QP = 2.2 cm

a,b,d