Which congruence rule applies? SSS, SAS, ASA, AAS, HL or not enough
Grade 10 Math Worksheet
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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 SAS.
- Yes, by HL.
- Not enough: this is SSA.
Tala checks two paper triangles: CH = QY = 13 cm, CW = QS = 8 cm and m∠H = m∠Y = 34°. Which rule proves them congruent, if any?
- Yes, by SSA.
- Yes, by HL.
- Yes, by SAS.
- Not enough: this is SSA.
Two triangles, not to scale, with the given angles marked and labeled. 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 AAA.
- Yes, by ASA.
- 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?
Jun checks two ladder braces. Right △GUW ≅ right △FHD by HL, with the right angle at G. UW = 53 cm and GU = 28 cm. How long is FD, 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?
- FG = VU
- DG = SU
- ∠G = ∠U
- 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?
- CQ = HY
- CW = HD
- CW = YD
- ∠C = ∠H
Pia checks two ladder braces. ∠V and ∠Q are right angles, and UV = DQ. Which one more fact proves △UVY ≅ △DQC by HL?
- UY = QC
- UY = DC
- VY = QC
- ∠Y = ∠C