Triangle Congruence Theorems

Who do I belong with?

100

△ ABC ≅ △ DEF: ∠B ≅ ∠__?

∠E

200

△ CAT ≅△ DOG : AT ≅ __?

OG

300

△ EFG ≅ △ HBD : ∠D ≅ ∠__?

∠G

400

△ BFG ≅ △ GTA : GT ≅ __?

BF

500

△ LFG ≅ △ MEH : HM ≅ __?

GL

Who am I?

100

If three sides of one triangle are congruent to three sides of another triangle, and the triangles are congruent. What is this method called?

What is SSS

200

If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, and the triangles are congruent. What is this method called?

What is SAS

300

If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, and the triangles are congruent. What is this method called?

What is ASA

400

If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, and the triangles are congruent. What is this method called?

What is AAS

500

This is NOT a universal method to prove triangles congruent because it cannot guarantee that one unique triangle will be drawn!! What method am I?

What is SSA

What’s my x? (Linear)

100

7x + 5 = 12x - 10

x = 3

200

4(x-5) = -8-2x

x = 2

300

5x - 6 = 7x - 2

x = -2

400

4x - 7 = 8x + 33

X = -10

500

2(2x +3) = -5x - 12

x = -2

What are my xs? (Quadratics)

100

x² + 9x + 18 = 0

x = - 6

x = -3

200

x² + 5x + 4 = 0

x = -4

x = -1

300

x² + 2x - 3 = 0

x = -3

x = 1

400

x² + 15x = -56

x = -7

x = -8

500

3x + 35 = x² + 5x

x = 5

X = -7

What do I equal?

100

△ ABC ≅ △ DEF

∠B = 46° , ∠E = ?

m∠E = 46°

200

△ HIK ≅ △ LFM

∠M = 22° , ∠K = ?

∠K = 22°

300

△ EFG ≅ △ MNO

FG = 2x + 10, NO = 5x + 4

What is the length of NO?

NO = 14

400

△ PED ≅ △ SAD

PD = 3x + 1, SD = -2x + 36

What is the length of SD?

SD = 22

500

△ BNM ≅ △ HJK

BM = 2(5x - 2), HK = 2x + 36

What is the length of BM?

BM = 46