- Now, the teams quiz each other.
- Each team needs to prove that their triangles are congruent.
- The other team can question and challenge any claims that the teammates use to justify congruency.
- When the team has successfully proven that their triangles are congruent, the team can draw either a flow
proof or a two- column proof with their statements and reasons in it.
III.MeetingObjectives
- Students will apply the ASA Congruence Postulate.
- Students will apply the AAS Congruence Postulate.
- Students will use these postulates to prove that their triangles are congruent.
IV.NotesonAssessment
- Question each team, were they successful in proving that their triangles are congruent?
- Is the proof written to show SSS, ASA, or AAS?
- Allow time for the students to share their work.
- Offer corrections when necessary.
Proof Using SAS and HL
I.SectionObjectives
- Understand and apply the SAS Congruence Postulate.
- Identify the distinct characteristics and properties of right triangles.
- Understand and apply the HL Congruence Theorem.
- Understand that SSA does not necessarily prove triangles are congruent.
II.ProblemSolvingActivity-TheWallDesign
- Here is the problem.
- “Harry has a square wall in his bedroom. He knows it is square because he has measured it. He decides to
paint a bold red diagonal down the wall. Harry starts at the upper right corner and measuring carefully, paints
a red diagonal from the upper right corner to the bottom left corner of the wall. He stands back to admire his
work. His brother comes in, looks at the wall and says, “It’s great, but your triangles aren’t even.” Harry says
that they are.” - Your task is to draw a diagram and write a two- column proof showing that Harry’s triangles are congruent.
Because Harry has not given us the dimensions of his wall, use the knowledge that it is square and decide your
own dimensions. - Allow time for the students to work on this task.
- If stuck, remind students that the triangles can be proved congruent using SAS. Refer them back to the text
for clarification and for right triangle properties. - Students need to show the measure of two sides, the measure of two angles to compare- these measurements
should be labeled in their diagrams.
III.MeetingObjectives
- Students will apply the SAS Congruence Postulate.
- Students will identify the distinct characteristics and properties of right triangles.
Chapter 5. Geometry TE - Problem Solving