Congruent Triangles Chapter 4-3. Lesson 3 CA Standard 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept.

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Presentation transcript:

Congruent Triangles Chapter 4-3

Lesson 3 CA Standard 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

Congruent Triangles Two triangles are congruent if all of their corresponding sides and corresponding angles are congruent.

Congruent Triangles A C B Y Z X  ABC   YXZ  A   Y  B   X  C   Z Congruent AnglesCongruent Sides AB  YX BC  XZ AC  YZ Order is important!!!

Lesson 3 Ex1 Corresponding Congruent Parts B. ARCHITECTURE A tower's roof is composed of congruent triangles all converging toward a point at the top. Name the congruent triangles. Answer: ΔHIJ  ΔKIL

Lesson 3 Ex1 Corresponding Congruent Parts A. ARCHITECTURE A tower's roof is composed of congruent triangles all converging toward a point at the top. Name the corresponding congruent angles and sides of

Lesson 3 CYP1 A. The support beams on the fence form congruent triangles. Which of the following congruence statements directly matches corresponding angles or sides ΔABC and ΔDEF? A. B. C. D.

Lesson 3 CYP1 A.ΔACB  ΔEDF B.ΔCBA  ΔFED C.ΔBCA  ΔDFE D.ΔBAC  ΔEFD B. The support beams on the fence form congruent triangles. Which statement correctly names the congruent triangles?

Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. If  A   D and  B   E, then  C   F. A C B D E F

 Congruence Properties Reflexive Property of   Every triangle is congruent to itself Symmetric Property of   If  ABC   DEF, then  DEF   ABC. Transitive Property of   If  ABC   DEF, and  DEF   JKL, then  ABC   JKL.

Lesson 3 Ex2 Transformations in the Coordinate Plane Use the Distance Formula to find the length of each side of the triangles. A. COORDINATE GEOMETRY The vertices of are R(─3, 0), S(0, 5), and T(1, 1). The vertices of ST are R(3, 0), S(0, ─5), and T(─1, ─1).

Lesson 3 Ex2 Transformations in the Coordinate Plane

Lesson 3 Ex2 Transformations in the Coordinate Plane

Homework Chapter 4-3 Pg 220: use the distance formula to show that the sides are congruent 20, 25-28, 39-41