Download Congruent Triangles

Congruent Triangles
September 30, 2009
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.