Quick Start Expectations 1.Fill in planner and HWRS HW: BPW p. 39, #7-18, #39 (ACE ws) 2.Get a signature on HWRS 3.On desk: protractor, journal, HWRS, pencil, pen 4.Warm Up: next slide… back of HWRS
Warm Up Not congruent, but SIMILAR! Yes! Slide C onto P, reflect across a vertical line.
No! AB is equal to DE, but they are not congruent. Angle A is congruent to angle D, but the triangles are clearly not congruent. One pair of corresponding parts is NOT enough.
No! AB = DE and AC = DF, but they are not congruent. No! If 2 pairs of angles are congruent, so is the third – but that doesn’t mean the triangles are congruent – different side lengths are possible! One pair of angles and one pair of sides does NOT mean the triangle is congruent. No!
Three pairs of congruent corresponding parts is often enough evidence to conclude 2 triangles are congruent, but it makes a difference what the combinations of parts are!! Angle – Side – Angle (ASA) Yes!
If 2 sides and the included angle of one triangle are congruent, respectively to 2 sides and the included angle of another triangle, then they are congruent! Included = between Side – Angle – Side (SAS)
Amy’s explanation isn’t quite complete. Yes, all the angles are congruent, but she doesn’t give any argument why the other sides are congruent, particularly HI an KL. Nor does she explain why the angles are matched.
GJLI and HKLI are parallelograms. Because HI is parallel to KL, angle H = angle K. Also, angle I = 180 – (angle G + angle H) Angle I = angle L
No! Congruence of angles does NOT guarantee congruence of triangles – even though it might look like it in this drawing! Congruent angles gives you similar triangles, but NOT congruent triangles!
Angle – Side – Angle (ASA) Side – Angle – Side (SAS) Side – Side – Side (SSS) Angle – Angle – Side (AAS) Included side Included angle Adjacent side Side – Side – Angle (SSA) is NOT a guarantee of congruence! - See Teaching Aid 2.3 Adjacent angle Angle – Angle – Angle (AAA) NOT a guarantee of congruence!
Not a simple answer… Why?