September 30, 2009 Congruent Triangles. Objectives Content Objectives Students will review properties of triangles. Students will learn about congruent.

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Presentation transcript:

September 30, 2009 Congruent Triangles

Objectives Content Objectives Students will review properties of triangles. Students will learn about congruent triangles. Language Objectives Students will describe the processes they used to solve problems involving triangles. Students will participate in class discussion, and ask clarifying questions when appropriate.

10. What is the measure of each angle of an equiangular triangle? Explain.

11. Is every equilateral triangle isosceles? Is every isosceles triangle equilateral? Explain.

12. The measure of one angle of a triangle is 115. The other two angles are congruent. Find their measures.

13. A right triangle has acute angles whose measures are in the ratio 1 : 2. Find the measures of these angles.

14. Two angles of a triangle measure 64 and 48. Find the measure of the largest exterior angle. Explain.

15. The ratio of the angle measures in triangle BCR is 2 : 3 : 4. Find the angle measures. What type of triangle is BCR?

What does it mean to be congruent? When two figures have the same shape and size, they are called congruent. We have already discussed congruent segments (segments with equal lengths) and congruent angles (angles with equal measures).

Congruent Triangles Triangles ABC and DEF are congruent. If you mentally slide triangle ABC to the right, you can fit it exactly over triangle DEF by matching up the vertices.

Definition of congruent triangles Two triangles are congruent if and only if their vertices can be matched up so that corresponding parts (angles and sides) of the triangle are congruent.

Describing parts of a triangle Angle R is opposite line segment SQ. Line segment SQ is included between angles S and Q. Angle S is opposite line segment QR. Angle Q is included between line segments QS and QR.

Postulate 12 Side-Side-Side (SSS) Postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Postulate 13 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 the triangles are congruent.

Postulate 14 Angle-Side-Angle Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Angle-Angle-Side (AAS) Theorem If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

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

Did we meet our objectives? Content Objectives Students will review properties of triangles. Students will learn about congruent triangles. Language Objectives Students will describe the processes they used to solve problems involving triangles. Students will participate in class discussion, and ask clarifying questions when appropriate.