5 Right TrianglesRight Triangles: side across from right angle is the hypotenuse, the remaining two are legs.The longest side of a right triangle is the hypotehuse.
6 Congruent Right Triangles 35There is one additional congruence rule that applies only to right trianglesThe two right triangles have two congruent sides, the hypotenuse and one legIs this enough information to show that the two triangles are congruent?Remember, SSA is not a congruence ruleSince ∆TEA and ∆CUP are both right triangles, we can use the Pythagorean Theorem to find the length of the other leg∆TEA ∆CUP by SSS (or SAS)44UCP35
7 Hypotenuse-Leg Congruence Theorem (HL) Words; 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..Symbols;ADIf ∆ABC and ∆DEF are right triangles, andHLBCFthen ∆ABC ∆DEFE
8 Examples OR A M hypotenuse leg hypotenuse P N C B leg A M hypotenuse
9 HL TheoremTo use the HL Theorem, you must show that three conditions are met.There are two right triangles.The triangles have congruent hypotenuses.There is one pair of congruent legs.
10 Example 1Is it possible to show that ∆JGH ∆HKJ using the HL Congruence Theorem? Explain your reasoning.SOLUTIONIn the diagram, you are given that ∆JGH and ∆HKJ are right triangles.By the Reflexive Property, you know JH JH (hypotenuse) and you are given that JG HK (leg). You can use the HL Congruence Theorem to show that ∆JGH ∆HKJ.10
11 Your Turn:Tell whether the pair of triangles is congruent or not and why.ANSWERYes; HL ≅ Thm.
12 Your Turn:Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.FGH, HJKANSWERHL ≅ Thm.
15 Does the diagram give enough information to show that the triangles are congruent? If so, state the postulate or theorem you would use.a.b.SOLUTIONa.From the diagram, you know that BAC DAC, B D, and BC DC. You can use the AAS Congruence Theorem to show that ∆BAC ∆DAC.15
16 b.From the diagram, you know that FG HG, EG EG, and EFG EHG. Because the congruent angles are not included between the congruent sides, you cannot show that ∆FGE ∆HGE.16
17 Does the diagram give enough information to show that the triangles are congruent? If so, state the postulate or theorem you would use.1.ANSWERyes; HL Congruence Theorem2.ANSWERnoANSWERyes; SSS Congruence Postulate, SAS Congruence Postulate, or HL Congruence Theorem3.
18 Is there enough given information to prove the triangles congruent Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.1.ABE, CBDANSWERSAS ≅ Post.
19 State a third congruence that would allow you to prove ΔRST ≅ ΔXYZ by the SAS Congruence postulate. 2.ST ≅ YZ, RS≅ XYANSWER∠S ≅ ∠Y
20 Joke Time What do you call a man who lives in an envelope? Bill. What dog can't bark?A hot dog.What do you call a monkey on a mine field?A Ba-Boom.