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Unit 1B2 Day 12 Do Now Fill in the chart: Acute Triangle # of Acute Angles # of Right Angles # of Obtuse Angles Right Triangle Obtuse Triangle Isosceles Triangles: Vocab. The two congruent sides are called the ________. The remaining side is called the _________. The two angles opposite the legs are called the __________ angles. The remaining angles is called the ___________ angle. Investigating Base Angles Use a straightedge to construct an acute isosceles (columns 1 and 3) or an obtuse isosceles (columns 2 and 4) triangle. Fold the triangle along a line that bisects the vertex angle. What do you observe about the base angles? Compare with someone next to you. Base Angles Theorem (Thm. 4.6) If two sides of a triangle are congruent, then the angles opposite them are _______________. If AB ≅ AC, then _________. B A C Base Angles Converse (Thm. 4.7) If two angles of a triangle are congruent, then __________________ __________________ B A If B ≅ C, then _______________ C Ex. 1: Proof of the Base Angles Thm. Given: AB ≅ AC Prove: B ≅ C B A C Corollaries Corollary to theorem 4.6—If a triangle is equilateral, then __________________. Corollary to theorem 4.7– If a triangle is equiangular, then _________________. A B C Ex. 2: Using Equilateral and Isosceles Triangles Find the values of x and y. Ex. 2a Find the values of x and y. Do now Find the value of x. Right Triangles For two right triangles, if both pairs of legs are congruent, then you can prove the triangles are congruent using ______. BUT there’s another way to prove right triangles are congruent… Hypotenuse-Leg (HL) 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 ________________ If BC ≅ EF and AC ≅ DF, then ∆ABC ≅ ∆DEF. MUST be right triangles! Ex. 3: Proving Right Triangles Congruent Given: AD CB, AC ≅ AB Prove: ∆ACD ≅ ∆ABD Ex. 4: Proving Right Triangles Congruent Given: AE EB, AE EC, AE The television antenna is perpendicular to the ED, AB ≅ AC ≅ AD. Prove: ∆AEB ≅ ∆AEC ≅ ∆AED ground. Each of the lines running from the top of the antenna to B, C, and D uses the same length of cable. More Examples Is there enough information to prove that the triangles are congruent? Explain! 6. 5. 7. Closure Can you use HL to prove that two isosceles triangles are congruent?