Congruent Triangles

September 30, 2009Congruent Triangles1ObjectivesContent ObjectivesStudents will review properties of triangles.Students will learn about congruent triangles.

Language ObjectivesStudents will describe the processes they used to solve problems involving triangles.Students will participate in class discussion, and ask clarifying questions when appropriate.2

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1110. What is the measure of each angle of an equiangular triangle? Explain.1211. Is every equilateral triangle isosceles? Is every isosceles triangle equilateral? Explain.1312. The measure of one angle of a triangle is 115. The other two angles are congruent. Findtheir measures.1413. A right triangle has acute angles whose measures are in the ratio 1 : 2. Find the measuresof these angles.1514. Two angles of a triangle measure 64 and 48. Find the measure of the largest exterior angle. Explain.1615. The ratio of the angle measures in triangle BCR is 2 : 3 : 4. Find the angle measures. What typeof triangle is BCR?17What 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).18Congruent TrianglesTriangles 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.

19Definition of congruent trianglesTwo 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.

20Describing parts of a triangleAngle 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.

21Postulate 12 Side-Side-Side (SSS) PostulateIf three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.22Postulate 13 Side-Angle-Side (SAS) PostulateIf 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.23Postulate 14 Angle-Side-Angle PostulateIf 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.24Angle-Angle-Side (AAS) TheoremIf two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.25HL TheoremIf the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

26Did we meet our objectives?Content ObjectivesStudents will review properties of triangles.Students will learn about congruent triangles.

Language ObjectivesStudents will describe the processes they used to solve problems involving triangles.Students will participate in class discussion, and ask clarifying questions when appropriate.27