Question

1. when triangle abc is reflected across line ab, the image is triangle abd. why is angle acd congruent to angle adb?

a. corresponding parts of congruent figures are congruent.
b. congruent parts of congruent figures are corresponding.
c. segment ab is a perpendicular bisector of segment dc.
d. an isosceles triangle has a pair of congruent angles.

1. which of the following criteria always proves triangles congruent? select all that apply. (lesson 2 - 11)

a. corresponding congruent side - side - angle
b. corresponding congruent side - angle - side
c. corresponding congruent angle - side - angle
d. 3 congruent angles
e. 2 congruent sides
f. 3 congruent sides

Explanation:

11.

Step1: Analyze reflection property

When a figure is reflected, the original and the image are congruent. So, \(\triangle ABC\cong\triangle ABD\).

Step2: Use congruent - figure property

For congruent figures, corresponding parts are congruent. \(\angle ACD\) and \(\angle ADB\) are corresponding parts of congruent figures \(\triangle ABC\) and \(\triangle ABD\).

12.

Step1: Recall congruence criteria

• SSA (Side - Side - Angle): SSA does not always prove triangles congruent. For example, in some cases, two different triangles can be formed with the same SSA measurements.
• SAS (Side - Angle - Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent (by the SAS criterion).
• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent (by the ASA criterion).
• Three congruent angles: Three congruent angles (AAA) only proves that the triangles are similar, not necessarily congruent.
• Two congruent sides: Two congruent sides (SS) do not prove triangle congruence. We need more information (like an included angle or another side).
• Three congruent sides (SSS): If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent (by the SSS criterion).

Answer:

1. A
2. B, C, F