SSS & HL

SSS & HL

by David Miller

​Lesson Information

You need: notes, pencil, scrap paper/space to solve equations​

standard:

MGSE9-12.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (Extend to include HL and AAS.)

​Essential Questions:

What information would you use to prioritize triangle congruence? 

How would you portray two congruent triangles?

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Multiple Choice

Which of the following describes a perpendicular bisector of a triangle?

• A segment that is perpendicular to the side of a triangle at its midpoint. Forms 90 degree angle

• A segment with endpoints at the vertex and midpoint of the opposite side.
• A segment that connects two midpoints of two sides.

Multiple Choice

If CB is 18, what is DC?

• 6

• 9

• 12

• 18

Multiple Choice

D is the midpoint of CB. Find the length of CB.

• BC = 4

• BC = 16

• BC = 12

• BC = 24

Multiple Choice

Which shows two triangles that are congruent by the SSS congruence theorem?

Multiple Choice

To prove that ΔDEF ≅ ΔDGF by SSS, what additional information is needed?

• ∠DEF ≅ ∠DGF

• ∠DFE ≅ ∠DFG 

• DE ≅ DG

• DG ≅ GF

Multiple Choice

For the triangles to be congruent by SSS, what must be the value of x?

• 1

• 3

• 6

• 8

1. must be right triangles

​2. Congruent legs

​3. congruent hypotenuses (the hypotenuse is across from the 90 degree angle)

​across from the 90

Multiple Choice

When can we use the HL Congruence Theorem?

• Right Triangles
• Isosceles Triangles
• When we have a reflexive side
• SSA

Multiple Choice

Which shows two triangles that are congruent by the HL congruence theorem?

Multiple Choice

Can the HL Congruence Theorem be used to prove the triangles congruent? If so, write a congruence statement.

• Yes, △ABC≅△NLM
• Yes, △CBA≅△NLM
• Yes, △CBA≅△MLN
• No

Multiple Choice

What additional information is required in order to know that the triangles are congruent by HL Theorem?

• ∠G ≅ ∠X
• ∠H ≅ ∠V
• GI ≅ XV
• GH ≅ XW

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• ASA
• Not Possible

Multiple Choice

Could ΔJKL be congruent to ΔXYZ? Explain.

• Yes, if JL ≅ XZ.

• Yes, if XZ = 10.

• No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.

• No, because the leg of one triangle is equal in length to the leg of the other triangle.

Multiple Choice

State if the triangles are congruent or not. If they are, state how you know.

• Yes - by SSS

• Yes - by ASA

• Yes - by HL

• Yes - by AAS

• Not congruent

Multiple Choice

State if the triangles are congruent or not. If they are, state how you know.

• Yes - by SSS

• Yes - by ASA

• Yes - by HL

• Yes - by AAS

• Not congruent

Multiple Choice

• ΔABC≅ΔDCB by HL
• ΔABC≅ΔDCB by SAS
• ΔABC≅ΔDCB by SSA
• ΔABC≅ΔDCB by SSS

Multiple Choice

How are these triangles congruent?

• SSS

• HL

• SAS

• AAS

Multiple Choice

How are these triangles congruent?

• SSS

• HL

• SAS

• ASA

Multiple Choice

For the triangles to be congruent by HL, what must be the value of x?

• 8

• 9

• 17

• 34

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• AAS
• Not Possible

Multiple Choice

The dotted line splits the parallelogram into two triangles. What is true about the congruency of the two triangles? 

• More information is needed.

• The triangles can be proven congruent using SSS.

• The triangles can be proven congruent using HL.

• The triangles are not congruent.

Multiple Select

Examine this figure.  Which two pieces of information, if true, would help to prove that ΔLMP ≅ ΔNMP by HL? Select two options.

• Point P is the midpoint of MK.

• Line MK is the perpendicular bisector of LN.

• ML ≅ MP

• ML ≅ MN

• PK ≅ PK

Multiple Choice

Which explains whether ΔFGH is congruent to ΔFJH?

• They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH

• They are congruent because opposite sides of a parallelogram are congruent.

• They are not congruent because only ONE pair of corresponding sides is congruent.

• They are not congruent because only two pairs of corresponding sides are congruent.

Multiple Choice

What value of x will make triangles ABM and DCM congruent by SSS?

• 3

• 5

• 7

• 9

Multiple Choice

For the triangles to be congruent by HL, what must be the value of x?

• 2

• 3

• 4

• 7

Multiple Choice

Are these triangles congruent? If so, state the rule which you used to determine congruence.

• SAS
• SSS
• Both SSS and SAS
• Not necessarily congruent

Multiple Choice

Which method will not prove triangles are congruent?

• ASA

• SAS

• SSA

• AAS

Multiple Choice

Which would be the best classification for the triangle shown?

• acute isosceles
• equiangular scalene
• equiangular isosceles
• equiangular equilateral

Multiple Choice

What is the value of x?

• 51
• 49
• 78

Multiple Choice

• 72
• 67
• 65
• 54

Multiple Choice

Find the value of x.

• 8

• 12

• 6

• 10

Multiple Choice

Find the value of x.

• -11

• 6

• 11

• -10