**HELLO**

I AM...

**CONSTRUCTING**

CONGRUENT TRIANGLES

CONGRUENT TRIANGLES

**ANGLES**

**CPCTC**

Theorems

WHAT

**POSTULATES**

TRIANGLES

GIVEN & PROVEN

WELCOME!

**I WANT**

ASA and AAS Theorems

HL Theorem

SHOULD BE

SIDES

GEOMETRY

1

2

3

**THE END**

**Sean Anthony Martinez**

martinezsean96@gmail.com

Geometry B2

1/12/13

martinezsean96@gmail.com

Geometry B2

1/12/13

Remember the theorems based off of the sides and angles

Make sure to use a compass to find and write points

Don't forget that AAA and SSA does not exist!!!

**I WILL BE**

**IN CHAPT. 4**

"Boxes aren't necessarily bad places to think in."

#1

Student

WHY SSA AND AAA WILL NOT WORK

ASA Postulate

Main: Triangles

SSS and SAS Postulates

Why AAA and SSA Will not Work

3 most Important notes to know

SEAN

MARTINEZ

**TO TALK**

Step 1: Draw a line segment with the Given length with the straight edge

The Given problem example would be to "construct an angle with the sides 5 inches, 6 inches, and 3 inches

Step 2: Set the width of your compass equal to another given side length

Step 3: Place the tip of the compass on one of the end points of the side AB (let's choose to place it on A) and draw an arc on either side of the line segment AB.

Step 4: Set the width of your compass equal to length of the third side, which is 4cm in this case.

Step 5: Place the tip of the compass on B and draw another arc which cuts the previously drawn arc at some point (say C).

Step 6: Join C to each of the points A and B to complete the triangle.

SSS POSTULATE

Side-Side-Side Postulate

If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent

If... AB=DE, BC=EF

SAS Postulate

Step 1: Construct an angle of the given measure (50o) in this case. Let's name the vertex of this angle as point A. Ensure that each of the arms of this angle are longer than the given two side lengths.

Step 2: Set the width of your compass equal to the one of the given side lengths. Let's set it equal to 5cm. Retain this width for the next step.

Step 3: Place the tip of the compass on the vertex of the 50o angle (point A) and draw an arc so as to cut any one of its arms at some point (say B).

Step 1: Start with the given line segment and two angles. Mark a point A that will be one vertex of the new triangle.

Step 2: Set the compasses' width to the length of the segment AB.

Step 4: Mark a point B on this arc. Then draw the line AB. This will be one side of the new triangle.

Step 5: With the compasses at any convenient width, draw an arc across both lines of the given angle A.

Step 6: Without changing the compasses' width, draw an arc at point A on the new triangle. The arc must cross AB

Step 7: Set the compasses to the arc width at the given angle A. This the distance between the points where the arc intersects the sides of the angle.

Step 1

Step 2

Step 3

Step 4

ANGLE-SIDE-ANGLE POSTULATE

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

If A=D, AC=DF,C=F

AAS Theorem

ANGLE-ANGLE-SIDE THEOREM

If two angles and a non-include side of one triangle are congruent to two angles and the corresponding non included side of another triangle, then the triangles are congruent

Uses the third angles theorem

AAA will not work because it can only make similar, but not congruent triangles

The angles are corresponding. but it cannot be truly true with the sides

They can then be any size

SSA will not work because the unknown side could be located in two different places and we can create two different triangles

Can only be true with right angles

Step 4: Set the width of your compass equal to the other given side length, which would be 7cm in this case.

Step 5: Place the tip of the compass on the vertex of the 50o angle (point A) and draw an arc so as to cut the other arm at some point (say C).

Step 6: Connect the points B and C.

Hypotenuse-Leg theorem

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

Step 1: Use the Pythagorean theorem or make sure there is a hypotenuse and a leg.

Step 2: make sure there is the angle-side-side angle with a right angle

Step 3: Do what other information is needed. In this case, what is needed to be known is CB=YZ

Then... ABC=DEF

SIDE-ANGLE SIDE Postulate

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

then... ABC=DEF

If... A=D, B=E, AC=DF

Then... ABC=DEF

HL THEOREM

WHAT IS TRIANGLE CONGRUENCE?

If two triangles are congruent they will have exactly the same three sides and exactly the same three angles.

Step 3: With the compasses' point on A, make an arc near the future vertex B of the triangle.

Step 8: Near point A draw an arc in a similar position so it crosses the arc drawn earlier. This, in effect, 'copies' the measure of the angle at P to the angle at A.

Step 9: Draw a line with a straight edge from A through the point where the arcs intersect. This will become the second side of the triangle. Draw it long.

Step 10: Repeat this process at B. Copying the angle measure from the given angle B to the new triangle at B. The point where the lines intersect is C, the third vertex of the triangle