1.24 Exploration

Below we have a triangle with two fixed 30° angles (angle-angle). Move point B to change the triangle.

Measure angle C. As you move point B, what happens to the measure of angle C?

Measure segments AB, BC, and CA. As you move point B, what happens to the measure of the segments?

Do you think that Angle-Angle (AA) is a valid triangle congruence criterion? In other words, if two triangles have two angles that are the congruent, can we guarantee that the two triangles are congruent?

Below we have a triangle with two fixed 30° angles and a fixed side of length 5 (angle-side-angle). Move point B to change the triangle.

Measure angle C. As you move point B, what happens to the measure of angle C?

Segment AB has a fixed length of 5. Measure segments BC and CA. As you move point B, what happens to the measures of the segments?

Do you think that Angle-Side-Angle (ASA) is a valid triangle congruence criterion? In other words, if two triangles have a consecutive angle, side, and angle that are congruent, can we guarantee that the two triangles are congruent?

Are triangles WYZ and WXY congruent? Why or why not?

No, they look different. Yes, they look the same. No, AA (angle-angle) is not a value congruence criterion. Yes, ASA (angle-side-angle) is valid!

1.24 Exploration

Below we have a triangle with two fixed 30° angles (angle-angle). Move point B to change the triangle.

Below we have a triangle with two fixed 30° angles and a fixed side of length 5 (angle-side-angle). Move point B to change the triangle.

Information: 1.24 Exploration