Congruent Congruent TrianglesTriangles

Congruent Congruent TrianglesTriangles

Chapter 4-3Chapter 4-3

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

AC

B

Y

Z

XABC YXZ

A Y

B X

C Z

Congruent Angles Congruent Sides AB YX

BC XZ

AC YZ

Order is important!!!

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

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

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.

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.

AC

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.

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).

Transformations in the Coordinate Plane

Transformations in the Coordinate Plane

HomeworkChapter 4-3• Pg 220:

6-910-13 use the distance formula to show that the sides are congruent

20, 25-28, 39-41