Triangle Congruence Theorems

When can you use the AAS postulate?

• You can use the AAS postulate when you know two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle.

• You can use the AAS postulate when you know three sides of one triangle are congruent to three sides of another triangle.

• You can use the AAS postulate when you know two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

• You can use the AAS postulate when you know one angle and two sides of one triangle are congruent to one angle and two sides of another triangle.

Provide an example of using the SSS postulate.

• If triangle STU has sides ST = 7 cm, TU = 5 cm, and SU = 9 cm, and triangle VWX has sides VW = 7 cm, WX = 5 cm, and VX = 9 cm, then triangles STU and VWX are congruent by SSS.

• If triangle ABC has sides AB = 6 cm, BC = 4 cm, and AC = 8 cm, and triangle DEF has sides DE = 6 cm, EF = 4 cm, and DF = 7 cm, then triangles ABC and DEF are congruent by SSS.

• If triangle GHI has sides GH = 3 cm, HI = 4 cm, and GI = 5 cm, and triangle JKL has sides JK = 3 cm, KL = 4 cm, and JL = 6 cm, then triangles GHI and JKL are congruent by SSS.

• If triangle MNO has sides MN = 5 cm, NO = 5 cm, and OM = 5 cm, and triangle PQR has sides PQ = 5 cm, QR = 5 cm, and PR = 4 cm, then triangles MNO and PQR are congruent by SSS.

What does AAS stand for in triangle congruence?

• Angle-Angle-Side

• Angle-Angle-Segment

• Angle-Side-Angle

• Side-Angle-Side

When can you use the SAS postulate?

• When you know two sides and the included angle of one triangle are congruent to two sides and the corresponding included angle of another triangle.

• When you know all three sides of one triangle are congruent to all three sides of another triangle.

• When you know two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle.

• When you know the perimeter of one triangle is equal to the perimeter of another triangle.

What is the significance of triangle congruence theorems?

• They provide criteria to determine if two triangles are congruent, which is essential in solving geometric problems.

• They are used to calculate the area of triangles.

• They help in identifying the types of triangles based on their angles.

• They are only applicable in right-angled triangles.

Provide an example of using the ASA postulate.

• If triangle ABC has angles A = 50°, B = 60° and side AB = 5 cm, and triangle DEF has angles D = 50°, E = 60° and side DE = 5 cm, then triangles ABC and DEF are congruent by ASA.

• If triangle XYZ has angles X = 40°, Y = 50° and side XY = 8 cm, and triangle PQR has angles P = 40°, Q = 50° and side PQ = 8 cm, then triangles XYZ and PQR are congruent by SSS.

• If triangle MNO has angles M = 45°, N = 45° and side MN = 7 cm, and triangle STU has angles S = 45°, T = 45° and side ST = 7 cm, then triangles MNO and STU are congruent by AAS.

• If triangle GHI has angles G = 30°, H = 70° and side GH = 10 cm, and triangle JKL has angles J = 30°, K = 70° and side JK = 10 cm, then triangles GHI and JKL are congruent by ASA.

Provide an example of using the AAS postulate.

• If triangle ABC has angles A = 50° and B = 60° and side AC = 5 cm, and triangle DEF has angles D = 50° and E = 60° and side DF = 5 cm, then triangles ABC and DEF are congruent by AAS.

• If triangle GHI has angles G = 30° and H = 60° and side GH = 4 cm, and triangle JKL has angles J = 30° and K = 60° and side JK = 4 cm, then triangles GHI and JKL are congruent by SSS.

• If triangle MNO has angles M = 40° and N = 70° and side MN = 6 cm, and triangle PQR has angles P = 40° and Q = 70° and side PQ = 7 cm, then triangles MNO and PQR are congruent by SAS.

• If triangle STU has angles S = 80° and T = 50° and side ST = 3 cm, and triangle VWX has angles V = 80° and W = 50° and side VW = 3 cm, then triangles STU and VWX are congruent by ASA.

When can you use the SSS postulate?

• You can use the SSS postulate when you know all three sides of one triangle are congruent to all three sides of another triangle.

• You can use the SSS postulate when you know two angles and one side of a triangle are congruent to another triangle.

• You can use the SSS postulate when you know one angle and two sides of a triangle are congruent to another triangle.

• You can use the SSS postulate when you know all three angles of one triangle are congruent to all three angles of another triangle.

What does HL stand for in triangle congruence?

• Hypotenuse-Leg

• Height-Length

• Half-Line

• Hypotenuse-Line

When can you use the ASA postulate?

• When you know two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle.

• When you know the lengths of all three sides of a triangle.

• When you know one angle and the lengths of the two adjacent sides of a triangle.

• When you know two sides and the angle opposite one of them.