Congruence

Steps to prove triangles congruent?

1. Mark the Given. 2. Mark ... Reflexive Sides / Vertical Angles 3. Choose a Method based on given/marked information. (SSS , SAS, ASA, HL, AAS) 4. List the Parts ... in the order of the method. 5. Fill in the Reasons ... why you marked the parts. 6. Write out the statement of congruence with the method as your reason

If two angles and a non included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.

Congruent by Angle, Angle, Side (AAS Postulate)

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

Congruent by Hypotenuse, Leg (HL Postulate)

If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the triangles are congruent.

Congruent by angle, side, angle (ASA Postulate)

If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent.

Congruent by side, angle, side (SAS Postulate)

If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

Congruent by side, side, side (SSS Postulate)

CPCTC=

Corresponding Parts of Congruent Triangles are Congruent

Proof for isosceles triangle?

Definition of isosceles triangle

What is the proof for midpoints to create two congruent segments (from the midpoint to each endpoint)?

Definition of midpoint

Proof for vertical angles?

Just write vertical angles

Proof for when the side is the same?

Reflexive side

Proof for all right angles are congruent?

Right Angle Congruence Theorem

Proof for triangles=180 degrees?

Triangle Sum Theorem

When information is given to you for the proof

Write given

Does the order of the letters to name the triangle matter?

Yes, the letters have to correspond. (See picture) For example it would be triangles BCA and FGE, not triangles BCA and GFE.

Does the order of the methods (ex: ASA) matter?

Yes. (See picture) For example ASA and AAS contain the same letters but on the triangle it is first the angle, then the side, and then another angle so it has to be ASA.

figures having the same SIZE and SHAPE

congruent

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are ___________

congruent (Third Angles Theorem)

In a triangle, the angle formed by two sides is the ______ _____ for the two sides.

included angle

The side of a triangle that forms a side of two given angles.

included side

CPCTC includes

perimeter median altitude area

Congruent figures can be

rotations, reflections or translations

What is the hypotenuse of a triangle?

the longest side of a right-angled triangle