Given: Triangle ABC is congruent to triangle XYZProve: Side AB is congruent to side XY (what postulate, theorem, or definition confirms that side AB is congruent to side XY?)

Corresponding parts of congruent triangles are congruent

Given: Side AB is congruent to side XY, side BC is congruent to side YZ, side AC is congruent to side XZ1. Do triangles ABC and XYZ have to be congruent based on the information above?2. If you said "No" to question #1, can triangles ABC and XYZ be congruent based on the information above?

1. Yes 2. No, they HAVE to be congruent

1. It depends on the type of triangle 2. Yes

Explain the HL Theorem.

On a pair of right triangles, if a leg of the right triangle (side touching the right angle) and the hypotenuse of the right triangle (side not touching the right angle) of two right triangles are congruent, then the triangles are congruent.

On a pair of right triangles, if two angles and a non-included side of the two triangles are congruent, then the triangles are congruent.

If the height and length of two triangles are congruent, then the triangles are congruent.

If two angles and two non-included sides of two triangles are congruent, then the triangles are congruent.

Given: Side AB is congruent to side XY, side BC is congruent to side YZ, angle C is congruent to angle ZAre triangles ABC and XYZ congruent?

It depends on if angles C and Z are obtuse or acute

Proving Triangles Congruent

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Questions and Answers

1.

Given: Triangle ABC is congruent to triangle XYZProve: Side AB is congruent to side XY (what postulate, theorem, or definition confirms that side AB is congruent to side XY?)
- A.
  
  Corresponding parts of congruent triangles are congruent
- B.
  
  ASA Postulate
- C.
  
  SAS Postulate
- D.
  
  SSS Posulate
- E.
  
  AAS Theorem
Correct Answer
A. Corresponding parts of congruent triangles are congruent

Explanation
As long as two triangles are congruent, then any sides or angles of the triangles are also congruent.

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2.

Given: In triangles ABC and XYZ, Angle A is congruent to angle X, side AB is congruent to side XY, and angle B is congruent to angle Y1. Prove: Triangle ABC is congruent to triangle XYZ2. Is the postulate you used valid? Does it work for any pair of triangles?
- A.
  
  1. AAS Theorem 2. Yes
- B.
  
  1. AAS Theorem 2. No
- C.
  
  1. ASA Postulate 2. Yes
- D.
  
  1. ASA Postulate 2. No
- E.
  
  1. SSA Postulate 2. No
Correct Answer
C. 1. ASA Postulate 2. Yes

Explanation
As long as two angles and the side between those angles are congruent on two triangles, then the two triangles are congruent.

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3.

Given: Side AB is congruent to side XY, side BC is congruent to side YZ, side AC is congruent to side XZ1. Do triangles ABC and XYZ have to be congruent based on the information above?2. If you said "No" to question #1, can triangles ABC and XYZ be congruent based on the information above?
- A.
  
  1. Yes 2. No, they HAVE to be congruent
- B.
  
  1. No 2. Yes
- C.
  
  1. No 2. No
- D.
  
  1. It depends on the type of triangle 2. Yes
Correct Answer
A. 1. Yes 2. No, they HAVE to be congruent

Explanation
The SSS postulate says that if three sides of two triangles are congruent, then the triangles are congruent. When we know that three sides are congruent, then the triangles HAVE TO be congruent. There's no way that three sides of two triangles can be congruent without the triangles being congruent.

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4.

Explain the HL Theorem.
- A.
  
  On a pair of right triangles, if two angles and a non-included side of the two triangles are congruent, then the triangles are congruent.
- B.
  
  On a pair of right triangles, if a leg of the right triangle (side touching the right angle) and the hypotenuse of the right triangle (side not touching the right angle) of two right triangles are congruent, then the triangles are congruent.
- C.
  
  If the height and length of two triangles are congruent, then the triangles are congruent.
- D.
  
  If two angles and two non-included sides of two triangles are congruent, then the triangles are congruent.
Correct Answer
B. On a pair of right triangles, if a leg of the right triangle (side touching the right angle) and the hypotenuse of the right triangle (side not touching the right angle) of two right triangles are congruent, then the triangles are congruent.
5.

Given: Side AB is congruent to side XY, side BC is congruent to side YZ, angle C is congruent to angle ZAre triangles ABC and XYZ congruent?
- A.
  
  Yes, they have to be
- B.
  
  Nope.
- C.
  
  It depends on if angles C and Z are obtuse or acute
- D.
  
  Possibly
Correct Answer
D. Possibly

Explanation
This defines the SSA postulate, which doesn't guarentee congruent triangles. However, if two sides and a non-included angle of a triangle are congruent, then there is a chance that the triangles are congruent.

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Jul 19, 2012

Quiz Created by
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Proving Triangles Congruent

Given: Triangle ABC is congruent to triangle XYZProve: Side AB is congruent to side XY (what postulate, theorem, or definition confirms that side AB is congruent to side XY?)

Given: In triangles ABC and XYZ, Angle A is congruent to angle X, side AB is congruent to side XY, and angle B is congruent to angle Y1. Prove: Triangle ABC is congruent to triangle XYZ2. Is the postulate you used valid? Does it work for any pair of triangles?

Given: Side AB is congruent to side XY, side BC is congruent to side YZ, side AC is congruent to side XZ1. Do triangles ABC and XYZ have to be congruent based on the information above?2. If you said "No" to question #1, can triangles ABC and XYZ be congruent based on the information above?

Explain the HL Theorem.

Given: Side AB is congruent to side XY, side BC is congruent to side YZ, angle C is congruent to angle ZAre triangles ABC and XYZ congruent?