Do Now Take out your compass and protractor.

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Presentation transcript:

Do Now Take out your compass and protractor. Put your 4.1/4.2 WS on your desk ready to be stamped. Draw ΔLMN in your notebook. Name the angles. L, M, N Write an “A” at each angle. Name the sides. LM, LN, MN Write an “S” at each side. Take out your compass and protractor. Put your 4.1/4.2 WS on your desk ready to be stamped. Draw ΔLMN in your notebook. Name the angles. Write an “A” at each angle. Name the sides. Write an “S” at each side. How many parts are in a triangle?

Error Analysis Compare your exit slip to Kathy’s

Are the Triangles Congruent? Congruence Shortcuts

Today’s Objectives Determine whether two triangles are congruent. Discover that SSS and SAS are valid congruence shortcuts but SSA is not. Discover that ASA and AAS are valid congruence shortcuts but AAA is not. Use problem solving skills.

Intro A building contractor has just assembled two massive triangular trusses to support the roof of a recreation hall. Before the crane hoits them into place, the contractor needs to verify that the two triangular trusses are identical. Must the contractor measure and compare all six parts of both triangles?

How much information would it take? How many pieces of information does a triangle have? What if I asked everyone in here to draw a triangle? Would everyone draw the same triangle? What if I told you one side had to be 5 cm? What if I told you that one side had to be 6 cm and one angle 40 degrees? What is the least amount of information I would have to give you for all of you to draw congruent triangles?

SSS Side-Side-Side Three pairs of congruent sides.

SAS Side-Angle-Side Two pairs of congruent sides and one pair of congruent angles (angles between the pair of sides)

ASA Angle-Side-Angle Two pairs of congruent angles and one pair of congruent sides (sides between the pairs of angles)

AAS Side-Angle-Angle Two pairs of congruent angles and one pair of congruent sides (sides not between the pairs of angles)

SSA Side-Side-Angle Two pairs of congruent sides and one pair of congruent angles (angles not between the pairs of sides)

AAA Angle-Angle-Angle Three pairs of congruent angles

Investigations We need to discover which cases turn out to be congruence shortcuts and which do not. Rules Each person in your group must construct their own triangle. Your triangle must have the 3 pieces of information you were assigned in order (side-angle-side for example) With your group, use the information given to you and see if you come up with congruent triangles or different triangles. Be ready to present your results.

Side Side Side (SSS) Postulate If three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

In other words… If you know this: Then you know this:

Side Angle Side (SAS) Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

In other words… If you know this: Then you know this:

Angle Side Angle (ASA) Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then these two triangles are congruent.

In other words… If you know this: Then you know this:

Angle Angle Side (AAS) Postulate If two angles and the non-included side one triangle are congruent to two angles and the non- included angle of another triangle, then these two triangles are congruent.

In other words… If you know this: Then you know this:

Side Side Angle (SSA) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are NOT NECESSARILY congruent.

In other words… If you know this: Then you don’t know if the triangles are congruent

Angle Angle Angle (AA) If two angles of one triangle are congruent to two angles of another triangle, then these two triangles are NOT NECESSARILY congruent.

In other words… If you know this: Then you don’t know if the triangles are congruent

Practice Are these two triangles congruent? If so, why? Name the congruent triangles. If not, why not? Order matters!

Practice

Practice

Congruency Shortcuts Review Shortcuts that show two triangles are congruent SAS SSS ASA AAS Shortcuts that don’t always work AA SSA

Today’s Objectives Determine whether two triangles are congruent. Discover that SSS and SAS are valid congruence shortcuts but SSA is not. Discover that ASA and AAS are valid congruence shortcuts but AAA is not. Use problem solving skills.

Exit Slip What type of information is given to you? Are these triangles congruent? Why/why not? List the congruency shortcuts that always work.

Honors Exit Slip 1. 2. For each figure to the right, determine if the triangles are congruent. If they are, write a proof. If they are not, explain why they are not.