Which congruence rule applies? SSS, SAS, ASA, AAS, HL or not enough
Grade 10 Math Worksheet
Circle the best answer, or write your answer on the line.
Two triangles, not to scale, with the given parts marked and labeled. Ren checks two rug triangles: DF = SU = 10 cm, FG = UV = 14 cm and m∠G = m∠V = 36°. Which rule proves them congruent, if any?
- Yes, by SSA.
- Yes, by HL.
- Not enough: this is SSA.
- Yes, by SAS.
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Two triangles, not to scale, with the given angles marked and labeled.
Zee checks two window panes: m∠G = m∠F = 45°, m∠Q = m∠D = 55° and m∠U = m∠C = 80°. Which rule proves △GQU ≅ △FDC, if any?
- Yes, by ASA.
- Yes, by AAA.
- Not enough: AAA fixes the shape, not the size.
Ari checks two boat sails: m∠S = m∠H = 30°, m∠V = m∠W = 64° and m∠Y = m∠G = 86°. Which rule proves △SVY ≅ △HWG, if any?
- Yes, by ASA.
- Yes, by AAA.
- Not enough: AAA fixes the shape, not the size.
Bo checks two ramp sides. Right △DFG ≅ right △VUS by HL, with the right angle at F. DG = 29 cm and DF = 20 cm. How long is US, in cm?
Esme checks two tower braces. Right △CHQ ≅ right △SWY by HL, with the right angle at H. CQ = 37 cm and HQ = 12 cm. How long is SW, in cm?
Kira checks two kite halves. Right △QSV ≅ right △YCG by HL, with the right angle at S. QV = 65 cm and SV = 33 cm. How long is YC, in cm?
Luz checks two tower braces. ∠F and ∠V are right angles, and DF = SV. Which one more fact proves △DFG ≅ △SVU by HL?
- ∠G = ∠U
- DG = SU
- FG = VU
- DG = SV
Milo checks two ramp sides. ∠Q and ∠Y are right angles, and QW = YD. Which one more fact proves △CQW ≅ △HYD by HL?
- CW = HD
- ∠C = ∠H
- CQ = HY
- CW = YD
Noah checks two tent flaps. ∠S and ∠F are right angles, and GS = UF. Which one more fact proves △GHS ≅ △UCF by HL?
- HS = CF
- ∠H = ∠C
- GH = UC
- GH = CF
Pia checks two ladder braces. ∠V and ∠Q are right angles, and UV = DQ. Which one more fact proves △UVY ≅ △DQC by HL?
- UY = DC
- ∠Y = ∠C
- VY = QC
- UY = QC