Do Now
• Are triangles ABC and DEF congruent?
• A(-2,-2) B(4,-2) C(4,6) and D(5,7) E(5,1) F(13,1)
– What types of lines make up the triangle?
Congruence
• How do we know if triangles are
congruent?
• What do we need to know about the
triangles in order to be able to assume
they are congruent?
Side Angle Side Congruence
Postulate
• If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of a second triangle, then
the two triangles are congruent.
Right Triangles
• Can we assume that the triangles are
congruent? Why?
Hypotenuse Leg Congruence
Theorem
• If the hypotenuse and a leg of a right
triangle are congruent to the hypotenuse
and a leg of a second right triangle, then
the two triangles are congruent.
Given: WY congruent to XZ, WZ perp. To ZY, and
XY perp. To ZY
Prove: Triangles WYZ and XZY are congruent
• WY congruent to XZ
• WZ perp. ZY, XY perp.
ZY
• Angles Z and Y are right
• Triangles WYZ and XZY
are right triangles
• ZY congruent to YZ
• Triangles WYZ and XZY
are congruent.
Given: WY congruent to XZ, WZ perp. To ZY, and
XY perp. To ZY
Prove: Triangles WYZ and XZY are congruent
• WY congruent to XZ
• WZ perp. ZY, XY perp.
ZY
• Angles Z and Y are right
• Triangles WYZ and XZY
are right triangles
• ZY congruent to YZ
• Triangles WYZ and XZY
are congruent.
• Given
• Given
• Def of Perpendicular
• Def of a right Triangle
• Reflexive Prop. Of
Congruence
• HL Congruence Thm