HONORS GEOMETRY
4.4. Proving Triangles Congruent (SSS, SAS)
Do Now:
• Prove that the polygons are congruent by identifying all
the congruent corresponding parts. Then write a
congruence statement
Homework
• Questions?
• Comments?
• Confusions?
• ASK ASK ASK
Well…..
• That was a pain! It takes so long to figure out whether
every single angle and side corresponds to another angle
and side.
• In triangles– is there an easier way?
Side-Side-Side (SSS) Congruence
• If three sides of one triangle are congruent to three sides
of a second triangle, then the triangles are congruent.
Example One:
Example Two:
You Try!
• Given: 𝑅𝑃 ≅ 𝑅𝑇; 𝑅𝑋 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 𝑃𝑇
• Prove: ∆𝑃𝑅𝑋 ≅ ∆𝑇𝑅𝑋
Included Angle
• The angle formed by two adjacent sides of a polygon.
Included Side
• Is the side located between two consecutive angles in a
polygon.
Example Three:
Side-Angle-Side (SAS) Congruence
• If two sides and the included angle of one triangle are
congruent to two sides and the included angle of a
second triangle, then the triangles are congruent.
Example Four: Congruent? Why?
Example Four (continued) SAS or SSS?
Example Five:
You Try!
Example Six:
Example Seven:
You Try!
• Given: 𝐸𝐺 ∥ 𝐷𝐹; 𝐸𝐺 ≅ 𝐷𝐹
• Prove: ∆𝐸𝐺𝐷 ≅ ∆𝐹𝐷𝐺
Practice Problems
• Try some problems on your own/in table groups
• As always call me over if you have questions!
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