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BELL RINGER Using CPCTC (corresponding parts of congruent triangles are congruent)… If Δ HOT ≅ Δ FUN, list the 3 sets of congruent sides and 3 sets of congruent angles.

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MORE ON TRIANGLE CONGRUENCE TUESDAY, NOVEMBER 5, 2013

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GRAPHIC ORGANIZER

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VOCABULARY Hypotenuse – the side across from the right angle in a right triangle Included – in-between Non-included – not in-between Bisect – cut in half (2 congruent parts) Vertical angles – angles across from each other when two lines intersect (always congruent). Reflexive Property – things are congruent to themselves

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THE PROBLEM (STRAIGHT FROM DPI) Andy and Javier are designing triangular gardens for their yards. Andy and Javier want to determine if their gardens that they build will be congruent by looking at the measures of the boards they will use for the boarders, and the angles measures of the vertices. Andy and Javier use the following combinations to build their gardens.

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Will these combinations create gardens that enclose the same area? If so, how do you know? If not, why? a. Each garden has length measurements of 12ft, 32ft and 28ft. b. Both of the gardens have angle measure of 110°, 25° and 45°. c. One side of the garden is 20ft another side is 30ft and the angle between those two boards is 40°. d. One side of the garden is 20ft and the angles on each side of that board are 60° and 80°. e. Two sides measure 16ft and 18ft and the non-included angle of the garden measures 30°. Let’s think about this… We’ll answer it a little later.

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Using “popsicle sticks” can you make 2 triangles that have the same angle measures but are not congruent? So, can two triangles be congruent by AAA? EXPERIMENT

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Using just 3 “popsicle sticks”, can you make 2 non-congruent triangles that have 2 congruent sides and a “non- included” congruent angle? So, does SSA work for congruent triangles? EXPERIMENT

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Will these combinations create gardens that enclose the same area? If so, how do you know? If not, why? a. Each garden has length measurements of 12ft, 32ft and 28ft. b. Both of the gardens have angle measure of 110°, 25° and 45°. c. One side of the garden is 20ft another side is 30ft and the angle between those two boards is 40°. d. One side of the garden is 20ft and the angles on each side of that board are 60° and 80°. e. Two sides measure 16ft and 18ft and the non-included angle of the garden measures 30°. Now we can answer these.

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PRACTICE Congruent Triangles Worksheet

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