Good Morning!

Please take out your homework from last night and your 4.4 review

worksheet and clear off your desks.

Objective: Prove triangles are congruent using a coordinate proof.Triangle ABC has points A(-3, 1), B(-5, -4), and C(-2, -5). Triangle PQR has points P(4, 7), Q(2, 2), and R(5, 1).Prove ∆ABC ∆PQR≅

First: Plot the points on a coordinate grid.

Now find the length of AB, AC, BC, PQ, QR, and PR using the distance formula.

Do you think architects have to measure all 3 angles and all 3 sides in one triangle to make sure it is congruent to another triangle? Or are there shortcuts?

In Lesson 4-4, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent.

Materials: You should each have a ruler, popsicle stick, and protractor, and pencil.

Use your pencil, popsicle stick, and ruler to create a triangle. Can you and your team members create two different triangles given equal side lengths? Or do your triangles always end up being exactly the same shape and size.

Remember: Just because your triangles are in a different orientation, does not mean they aren’t congruent.

You only need to know that two triangles have three pairs of congruent corresponding sides. This can be expressed as the following postulate.

First shortcut: SSS

To create this play dome, the directions don’t specify angle measures because if all the stick pieces are congruent, the triangles are automatically congruent. There is only one possible triangle you can make.

An included angle is an angle formed by two adjacent sides of a polygon.B is the included angle between sides AB and BC.

Let’s check if SAS works.

http://www.geogebratube.org/student/m5253

• Materials: Ruler, sharpened pencil, protractor, sheet of paper.

• Procedure: Measure a line segment that is 6 inches long.

• Create a 65 degree angle with the line.• Make the other ray 7 inches long.

• Is there only one possible triangle you can make?

Let’s check if AAA works?

• If three angles in one triangle correspond to three angles in another triangle, are the triangles automatically congruent?

• Why or why not?

http://tube.geogebra.org/student/m26172

Which postulate, if any, can be used to prove the triangles congruent?

1. 2.

3. 4.

Quick Check

Apply SSS and SAS to construct triangles and solve problems.

Prove triangles congruent by using SSS and SAS.

Objectives