5.4 Equilateral & Isosceles Triangle and 5.5 SSS & HL Congruence

5.4 Equilateral & Isosceles Triangle and 5.5 SSS & HL Congruence

by Mary Lett

​Objective and Standards

• ​Students will be able to prove special relationships about equilateral triangles, isosceles triangles, and using SSS and HL.

• ​HSG-CO.C.10, HSG-CO.D.13, HSG-MG.A.1, HSG-CO.B.8, HSG-MG.A.1, HSG-MG.A.3

​Parts of an Isosceles Triangle

• ​Legs: the congruent sides of the triangle

• ​Vertex angle: the angle formed by the legs

• ​Base: the third side of the triangle

• ​Base Angles: the angles formed by the base and each leg

Fill in the Blanks

What is the

$m\angle U$  ?

Fill in the Blanks

What is the

$m\angle T$  ?

Fill in the Blanks

What is the measure of

$EF$  ?

Fill in the Blanks

What is 

$m\angle F$  ?

Fill in the Blanks

Find the value of x.

​Parts of a Right Triangle

• ​Hypotenuse: the side across from the right angle

• ​Legs: the sides that form the right angle

Multiple Choice

• ΔABC≅ΔBED by SAS

• ΔABC≅ΔBED by SSS

• ΔACB≅ΔDEB by SAS

• ΔACB≅ΔDEB by SSS

Multiple Choice

• Congruent by ASA

• Congruent by SAS

• Congruent by SSS

• Not Necessarily Congruent

Multiple Choice

• ΔABC≅ΔDCB by HL

• ΔABC≅ΔDCB by SAS

• ΔABC≅ΔDCB by SSA

• ΔABC≅ΔDCB by SSS

Multiple Choice

• ΔPQT≅ΔSRT by HL

• ΔPQT≅ΔSRT by SAS

• ΔPQT≅ΔSRT by SSA

• ΔPQT≅ΔSRT by SSS

Multiple Choice

• ΔLMN≅ΔSTU by HL

• ΔLMN≅ΔSTU by SAS

• ΔLMN≅ΔSTU by SSA

• ΔLMN≅ΔSTU by SSS

Multiple Choice

• ∠B≇∠E and ∠C≇∠F

• ∠C≇∠F and AC≇DF

• ∠B≇∠E and AC≇DF

• ∠B≇∠E and ∠C≇∠F and AC≇DF