Unit 1B2 Day 12

  Fill in the chart: Do Now Acute Triangle Right Triangle Obtuse Triangle # of Acute Angles # of Right Angles # of Obtuse Angles

 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.

  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. Investigating Base Angles

 Base Angles Theorem (Thm. 4.6)  If two sides of a triangle are congruent, then the angles opposite them are _______________.  If AB ≅ AC, then _________.

 Base Angles Converse (Thm. 4.7)  If two angles of a triangle are congruent, then __________________ __________________  If  B ≅  C, then _______________

 Ex. 1: Proof of the Base Angles Thm.  Given: AB ≅ AC  Prove:  B ≅  C

 Corollaries  Corollary to theorem 4.6—If a triangle is equilateral, then __________________.  Corollary to theorem 4.7– If a triangle is equiangular, then _________________.

 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  The television antenna is perpendicular to the ground.  Each of the lines running from the top of the antenna to B, C, and D uses the same length of cable. Given: AE  EB, AE  EC, AE  ED, AB ≅ AC ≅ AD. Prove: ∆AEB ≅ ∆AEC ≅ ∆AED

 More Examples  Is there enough information to prove that the triangles are congruent? Explain!

 Closure  Can you use HL to prove that two isosceles triangles are congruent?