Proving Triangle Congruence on the Coordinate Plane

Mr. Allen introduces congruent triangles on the XY coordinate plane, discussing methods like side-side-side, side-angle-side, and others. He demonstrates calculating side lengths using the distance formula and Pythagorean theorem, verifying congruence through these calculations. The video explores alternative scenarios with given angles and different congruence criteria, concluding with tips on congruence and coordinate geometry.

Which of the following is NOT a method to determine triangle congruence?

• Angle-Angle-Angle (AAA)

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Hypotenuse-Leg (HL)

What is the preferred method of the instructor for finding distances on the XY coordinate plane?

• Counting horizontally

• Using a ruler

• Pythagorean theorem

• Distance formula

What is the side length between points (1, 8) and (8, 8) on the XY coordinate plane?

• 6

• 7

• 9

• 8

What is the length of side AC if the coordinates are (1, 8) and (3, 2)?

• Square root of 40

• Square root of 61

• Square root of 25

• Square root of 36

What is the length of side BC if the coordinates are (3, 8) and (8, 2)?

• Square root of 61

• Square root of 40

• Square root of 25

• Square root of 36

What is the length of side DF if the coordinates are (-1, 8) and (3, 2)?

• Square root of 61

• Square root of 36

• Square root of 25

• Square root of 40

What is the length of side EF if the coordinates are (3, 8) and (8, 2)?

• Square root of 40

• Square root of 25

• Square root of 36

• Square root of 61

By which method are triangles ABC and DF proven to be congruent?

• Hypotenuse-Leg (HL)

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

If angle B is congruent to angle E, which method can be used to prove triangle congruence?

• Angle-Side-Angle (ASA)

• Hypotenuse-Leg (HL)

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

What additional information might be given to simplify proving triangle congruence?

• Measure of one angle

• Area of one triangle

• Length of one side

• Coordinates of one point