Today was the real beginning of our Triangle Unit (AKA delving into deductive proof).
We started with a sketch of a triangle with a line through one vertex that is parallel to the opposite side. Students discussed a plan for explaining why this could lead to The sum of the angles of a triangle is 180 degrees. We then created a deductive proof of the Triangle Sum Theorem from what students shared.
Then we did patty paper investigations for C-18-19: If a triangle is isosceles then its base angles are congruent. And 19 is the converse: if a triangle has two equal angles, then it is isosceles.
We wrote up C17-19 in GT. See attachment for both of these pages.
A grade was taken on HW #7; then we shared answers and discovered a new idea: an exterior angle of a triangle is the sum of the two angles on the other side.
We then practiced explaining deductively: If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. An exterior angle of a triangle is the sum of its two remote interior angles.
HW #8: p 214: 1-10, 14-15, p 224: 10-11.
You can also write up more Geometric Truth from the attachment below that has definitions for triangle angles and C-22 - Triangle Exterior Angle Theorem.
All but 2nd period got to view their tests. Make-ups need to be taken ASAP.
We started with a sketch of a triangle with a line through one vertex that is parallel to the opposite side. Students discussed a plan for explaining why this could lead to The sum of the angles of a triangle is 180 degrees. We then created a deductive proof of the Triangle Sum Theorem from what students shared.
Then we did patty paper investigations for C-18-19: If a triangle is isosceles then its base angles are congruent. And 19 is the converse: if a triangle has two equal angles, then it is isosceles.
We wrote up C17-19 in GT. See attachment for both of these pages.
A grade was taken on HW #7; then we shared answers and discovered a new idea: an exterior angle of a triangle is the sum of the two angles on the other side.
We then practiced explaining deductively: If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. An exterior angle of a triangle is the sum of its two remote interior angles.
HW #8: p 214: 1-10, 14-15, p 224: 10-11.
You can also write up more Geometric Truth from the attachment below that has definitions for triangle angles and C-22 - Triangle Exterior Angle Theorem.
All but 2nd period got to view their tests. Make-ups need to be taken ASAP.
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