Sections 4.3 - 4.5

Triangle Congruence

Similar Triangles

We know from previous sections, that two triangles are similar if:

AA (2 sets of corresponding angles are congruent)

SAS (2 corresponding sides have the same scale factor and one set of angles between the 2 sides are congruent)

SSS (3 sets of corresponding sides are proportional)

If 3 sides of one triangle are congruent to 3 sides of another, then the 2 triangles are congruent.

SSS

If the corresponding sides of two triangles are proportional (all have the same scale factor), then the triangles are ___________.

If the corresponding sides of two triangles are congruent (S.F. = 1), then the triangles are ___________.

a. b.

SSS:Decide whether or not the

congruent statement is true by SSS. Explain your reasoning.

6

If 2 sides and the included angle of a triangle are congruent to the corresponding parts of another, then the triangles are congruent.

SAS

If 2 sets of corresponding sides proportional (all have the same scale factor) and 1 set of corresponding angles are congruent, then the triangles are ___________.

If the corresponding sides of two triangles are congruent (S.F. = 1), then the triangles are ___________.

SAS:Decide whether or not the congruent statement is true by SAS. Explain your reasoning.

c. d.

Yes No

If 2 angles and the included side of a triangle are congruent to the corresponding parts of another, then the triangles are congruent.

c. d. A

B

E

C

D

ASA: Decide whether or not the congruent statement is true by ASA. Explain your reasoning.

If 2 angles and the non- included side of a triangle are congruent to the corresponding parts of another, then the triangles are congruent.

AAS:

NOYes ASA

Decide whether or not the congruent statement is true by AAS. Explain your reasoning.

c. d.

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

Leg:

Hypotenuse: Longest side of a right triangle and opposite the right angle

2 shorter sides of a right triangle

B) B and D are both right angles. C is the midpoint of .

A)BD

HL:Decide whether there is enough information to prove that the two triangles are congruent by using HL theorem.

SSA / ASS

On Your Own 5:Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.

1. is TSW WVT? 2. 3.

Warm Up:

Use the diagram to name the included angle between the given pair of sides.

a. b. c.H HIG HGI

On Your Own 2:

Use the diagram to name the included angle between the given pair of sides.

a. b. c.GIJ HGI J

EXTRA PRACTICE

Explain how you can prove that the indicated triangles are congruent using the given postulate or theorem.a.

b.

c.

Practice problemsState the third congruence that is needed to prove that ∆ DEF ∆ ABC, using the given postulate or theorem.

1.

2.

3.

Tell whether you can use the given information to show that

∆ JKL ∆ RST.

4.5.6.7.

NO

Yes AAS

Yes ASA

NO