**Chapter 4 : Proving Triangles Congruent**

1. Journal

Identify three methods for proving that trianlges are congruent and explain when to use each method. Write example triangle pairs that illustrate when to use each method.

**2. Multi-Step Problem**

The figure at the right shows a cabin at a campground. Use the figure to answer the questions that follow.

**Problem Solving Part 2**

c. I dentify all corresponding parts.

HL

Hypoteneus - Leg Congruence Theorem

When should you use HL?

HL should only be used in the presence of two right triangles. In other words, if you see two right angles from to different triangles, use HL.

Hypoteneus

Leg

Leg

Example:

A

B

C

D

E

F

Given:

ABC and DEF are right triangles.

AB DE

BC EF

By HL, we can conclude that ABC DEF

If the hypoteneus and a leg of a right triangle are congruent to those of another, then the two triangles are congruent.

ASA

Angle - Side - Angle Congruence Postulate

When should you use ASA?

When there are two angles that are given congruent and an included side is congruent.

Example:

A

B

C

D

E

F

Given:

A D

AC DF

C F

By ASA, we can conclude that ABC DEF.

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

≅

AAS

Angle - Angle - Side Congruence Postulate

When should you use AAS?

You should use AAS when there are two angles and a non-included side of two triangles given congruent.

Example:

A

B

C

D

E

F

Given:

A D

C F

BC EF

By AAS, we can conclude that ABC DEF.

If two angles and a non-included side of one trianlge is congruent to those of another, then the two triangles are congruent.

A

B

C

D

E

F

G

a. Identify each triangle in the figure by its angles and by its sides:

ABD: right triangle ; scalene

DBC: right triangle ; scalene

ABC: obtuse triangle ; isoceles

FGE: obtuse triangle ; scalene

Statements

Reasoning

1. AB BC ; ABD and CBD are 1. Given

right angles.

2. ABD and CBD are right 2. Definition of right angles in triangles

triangles.

3. BD DB 3. Reflexive Property

4. ABD CBD 4. HL

b- Prove that ABD is congruent to CBD.

A C

BD DB

AB BC

DA DC

ABD BDC

DBA CBD

d. Suppose that m BAD 33. Find the measure of ABC.

Statement:

Reason:

1. m BAD= 33 1. Given

2. A C 2. CPCT

3. A+ B+ C 3. Triangle Sum Theorem

4. A= 33 + m B+ m C= 4. Subtraction Property of Equality

180; 33+ m B+ 33= 180

5. 180- 66= m B 5. Subtraction Property

6. 114 = m B 6. Simplification Property

e. A design of two triangles will be put on the side of the cabin

as a decorative element. One triangle that will be used is shown

in the figure. Draw the other triangle in the design by using the

transformation (x,y) (-x,y).

C (-1,1)

B (0,4)

A (-3,0)

y

x

f. What kind of transformation did you perform in

part (e)?

Reflection on the y-axis

g. Explain how you can show that the two triangles are congruent

to verify that the transformation is a congruent transformation.

You could measure the sides.

You could measure the angles.

The cabin at the campground uses electricity that can be generated from

a variety of sources:

1. List the different sources of energy that can be used.

Solar Energy

Hydroelectricity

Wind power

Power generator

Propane

2. What is the environmental impact of this energy sources?

Why might they use these sources?

-Solar Energy is energy from the sun, so it doesn't effect the environment much.

-Hydroelectricity is energy from water that turns turbines to produce energy. It can effect the life of fish in the water source.

-Wind energy is another option, but not a universal option, because it depends on the amount of wind that is available

in the area.

-There are many ways to get electricity without effecting the environment like we mentioned.

Thank You!