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To prove triangles congruent using the HL Theorem

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Presentation on theme: "To prove triangles congruent using the HL Theorem"β€” Presentation transcript:

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2 To prove triangles congruent using the HL Theorem
Students will use SSA to prove right triangles congruent and will use counterexamples of non-right triangles to find why SSA is not a universal rule. To prove triangles congruent using the HL Theorem

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10 Statements Reasons 𝐢𝐷 β‰… 𝐸𝐴 , 𝐴𝐷 𝑖𝑠 π‘π‘’π‘Ÿπ‘‘π‘’π‘›π‘‘π‘–π‘π‘’π‘™π‘Žπ‘Ÿ π‘π‘–π‘ π‘ π‘’π‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ 𝐢𝐸 Given ⊿𝐢𝐡𝐷 π‘Žπ‘›π‘‘ ⊿𝐸𝐡𝐴 π‘Žπ‘Ÿπ‘’ π‘Ÿπ‘–π‘”β„Žπ‘‘ π‘‘π‘Ÿπ‘–π‘Žπ‘›π‘”π‘™π‘’π‘  Definition of βŠ₯π‘π‘–π‘ π‘’π‘π‘‘π‘œπ‘Ÿ 𝐢𝐡 β‰… 𝐸𝐴 Definition of βŠ₯π‘π‘–π‘ π‘’π‘π‘‘π‘œπ‘Ÿ ⊿𝐢𝐡𝐷 β‰…βŠΏπΈπ΅π΄ HL

11 4-6 Quiz The following questions are designed to help you determine if you understood today’s lesson Please record the number you get right on your portfolio sheet If you do not understand why you missed one of the problems make sure you find time to come and ask me!

12 I only II only III only II and III
1. For which situation could you prove βˆ†1  βˆ†2 using the Hypotenuse-Leg Theorem? I only II only III only II and III

13 No, the triangles cannot be proven congruent.
2. Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement? Yes; βˆ†CAB  βˆ†DAC Yes; βˆ†ACB  βˆ†ACD Yes; βˆ†ABC  βˆ†ACD No, the triangles cannot be proven congruent.

14 A  E mBCE = 90 AC  DC AC  BD
3. What additional information will allow you to prove the triangles congruent by the HL Theorem? A  E mBCE = 90 AC  DC AC  BD

15 HL, AAS, ASA, and SAS HL, AAS, and ASA HL and ASA
4. 𝐢𝐡 is perpendicular to 𝐴𝐷 at B between A and D. ∠DAC β‰Œ ∠ADC. By which of the five congruence statements, HL, AAS, ASA, SAS, and SSS, can you conclude Ξ”ABC β‰ŒΞ”DBC? HL, AAS, ASA, and SAS HL, AAS, and ASA HL and ASA HL, AAS, ASA, SAS, and SSS

16 SQ  PR PS  RS PQ  RQ SQ  SQ
5. Is βˆ†PQS  βˆ†RQS by HL? If so, name the legs that allow the use of HL. SQ  PR PS  RS PQ  RQ SQ  SQ

17 Then rate your assignment
4-6 p. 262 – #8-24 even Then rate your assignment as to how well you understood the lesson and write why you rated yourself that way.


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