Section 4.6Isosceles, Equilateral, and Right Triangles

Section 4.6 Isosceles, Equilateral, and Right Triangles

OBJECTIVES: To use and apply properties of isosceles and equilateral triangles To prove right triangles congruent using the Hypotheses Leg Theorem

BIG IDEA: Reasoning and Proof ESSENTIAL UNDERSTANDINGS:  The angles and sides of isosceles and equilateral triangles have special relationships.  Another way triangles can be proven to be congruent is by using one pair of right angles, a pair of hypotenuses, and a pair of legs. MATHEMATICAL PRACTICE: Construct viable arguments and critique the reasoning of others

Isosceles Triangle: a triangle with at least two ______sides

If an Isosceles triangle has exactly two congruent sides, then

: the two angles ______to the base are called ______and

: the angle ______the base is called ______

Base Angles Thm: If ______sides of a triangle are ______, then the angles ______them are congruent.

Converse of the Base Angles Thm: If ______angles of a triangle are ______, then the sides ______them are congruent.

EX: Given: Prove:

EX: Find the value ofand

Corollary to Base Angles Thm: If a triangle is ______, then it is ______Corollary to Base Angles Converse Thm: If a triangle is equiangular, then it is equilateral.

EX: Find the value ofand

EX: Find the unknown measure(s). Tell what theorems you used. X a) b) c)

Hypotenuse-Leg (HL) Thm: If the ______and a ______of a ______triangle are congruent to the hypotenuse and a leg of a ______right triangle, then the two triangles are ______

EX: Determine whether you are given enough info to prove that the triangles are congruent. a) b) c) M P L N B

N Q P O L T K

EX: Given: Prove: B

ASSIGNMENT: p. 239 8, 10 – 16 all, 18 – 24 evens, 34, 45 – 57x3