<p>Section 4.6 Isosceles, Equilateral, and Right Triangles</p><p>OBJECTIVES: To use and apply properties of isosceles and equilateral triangles To prove right triangles congruent using the Hypotheses Leg Theorem</p><p>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</p><p>Isosceles Triangle: a triangle with at least two ______sides</p><p>If an Isosceles triangle has exactly two congruent sides, then</p><p>: the two angles ______to the base are called ______and</p><p>: the angle ______the base is called ______</p><p>Base Angles Thm: If ______sides of a triangle are ______, then the angles ______them are congruent.</p><p>Converse of the Base Angles Thm: If ______angles of a triangle are ______, then the sides ______them are congruent.</p><p>EX: Given: Prove:</p><p>EX: Find the value ofand</p><p>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.</p><p>EX: Find the value ofand</p><p>EX: Find the unknown measure(s). Tell what theorems you used. X a) b) c)</p><p>Z Y</p><p>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 ______</p><p>EX: Determine whether you are given enough info to prove that the triangles are congruent. a) b) c) M P L N B</p><p>M Q R</p><p>N Q P O L T K</p><p>EX: Given: Prove: B</p><p>A C D</p><p>ASSIGNMENT: p. 239 8, 10 – 16 all, 18 – 24 evens, 34, 45 – 57x3</p>