Good morning! Get out, Activity: Informal Triangle Congruence and a writing utensil.

Transcription

1 Good morning! Get out, Activity: Informal Triangle Congruence and a writing utensil. AGENDA: 1) Compare and Discussion Activity: Informal Triangle Congruence o informal inductive 2) Activity: Deductive Triangle Congruence HOMEWORK: HW: Informal Triangle Congruence and finish Activity: Deductive Triangle Congruence GEOMETRY SEC 1 Nov. 15

2 Joey s creative solution!

3 8) It s a parallelogram. Explanations may vary. Since sides FL and TA are parallel, the perpendicular bisectors of those sides will be parallel to each other (AIA). The same logic applies for the other two sides. Tony: The smaller parallelogram is also similar to FLAT (justification was stated in class).

4 When are two triangles congruent? Within your group, compare your drawings and jot down conclusions to answer the questions. You may use patty paper to compare triangles. Please use the same patty paper and just erase the triangle once you re done with a problem. #6 should read: In ABC and XYZ given below, label A X, B Y, and BC YZ. Is ABC XYZ? Explain your answer.

5 Side-Side-Side (SSS): If the three sides of one triangle are congruent to the three sides of another triangle, what can we conclude? The triangles are congruent. This is known as the Side-Side-Side Triangle Congruence Theorem (SSS).

6 Side-Angle-Side (SAS): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, what can we conclude? The triangles are congruent. This is known as the Side-Angle-Side Triangle Congruence Theorem (SAS).

7 Angle-Side-Angle (ASA): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, what can we conclude? The triangles are congruent. This is known as the Angle-Side-Angle Triangle Congruence Theorem (ASA).

8 Side-Side-Angle (SSA): If two sides and a non-included angle of one triangle are congruent to two sides and a nonincluded angle of another triangle, what can we conclude? The triangles are not always congruent, because two different triangles are possible. Therefore, there is no Side-Side-Angle congruence theorem.

9 Example for #4) So SSA is not a triangle congruence theorem.

10 Angle-Angle-Angle (AAA): If three angles of one triangle are congruent to three angles of another, what can we conclude? The triangles are not always congruent, because there are an infinite number of possible triangles of different side lengths with those angle measures. Therefore, there is no Angle-Angle-Angle congruence theorem.

11 Angle-Angle-Side Triangle Congruence Theorem (AAS): If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, what can we conclude? The triangles are congruent. This is known as the Angle-Angle-Side Triangle Congruence Theorem (AAS). The AAS Congruence Theorem follows directly from the _ASA_ Congruence Theorem.

12 #6)

13 If two angles in one triangle are congruent to two angles in another, then the third pair of angles are congruent, i.e. C Z. So we now have two angles and the included side of one triangle congruent to two angles and the included side of another. By the ASA Congruence Theorem, ABC XYZ. The AAS Congruence Theorem follows directly from the ASA Congruence Theorem.

14 Which of these are true?

15 Included Included angle: angle included between two sides of a triangle Included side: a side that is included between two angles of a triangle

16 Activity: Deductive Triangle Congruence Use the triangle congruence theorems, along with other properties, to prove that given triangles are congruent. Reflexive Property: a number is equal to itself.

17 Deductive Triangle Congruence s See student work on the next slide. Notice that Yoyo proved that the two triangles were congruent a different way and used AAS. The order in which you write the letters for the triangles doesn t necessarily matter, but the order for the naming of both triangles must be consistent. This ensures that corresponding angles and sides match up and are truly congruent. (Sara)

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19 TYPED UP PROOFS: ANOTHER PROOF:

20 Homework Complete HW: Informal Triangle Congruence and finish Activity: Deductive Triangle Congruence TURN IN ON MON, NOV. 18: *Activity: Informal Triangle Congruence *HW: Informal Triangle Congruence *Activity: Deductive Triangle Congruence We ll go over this activity in class