Questions: Select all the statements that must be true. O. Points B, A, and F are collinear. B. The measure of angle BCA is the same as the measure of Line AD is parallel to line BC. D. The measure of angle CED is the same as the measure The measure of angle DAC is the same as the measure F. Triangle ADC is a reflection of triangle FAD.

Select all the statements that must be true.
O. Points B, A, and F are collinear.
B. The measure of angle BCA is the same as the measure of

Line AD is parallel to line BC.
D. The measure of angle CED is the same as the measure

The measure of angle DAC is the same as the measure
F. Triangle ADC is a reflection of triangle FAD.

Transcript text: Select all the statements that must be true. O. Points $B, A$, and $F$ are collinear. B. The measure of angle $B C A$ is the same as the measure of Line $A D$ is parallel to line $B C$. D. The measure of angle $C E D$ is the same as the measure The measure of angle $D A C$ is the same as the measur F. Triangle $A D C$ is a reflection of triangle $F A D$.

Solution

Solution Steps

Step 1: Analyze the given information

Triangles FAD and DCE are translations of triangle ABC. This means that corresponding angles and sides of these triangles are congruent.

Step 2: Evaluate statement A

Points B, A, and F are collinear. Since FAD is a translation of ABC, and translations don't change the relative positions of the vertices within a shape, F cannot lie on the line segment BA. Hence, this statement is false.

Step 3: Evaluate statement B

The measure of angle BCA is the same as the measure of angle ECD. Since triangle DCE is a translation of ABC, the corresponding angles are congruent: ∠BCA ≅ ∠DCE. Hence, this statement is false since ECD is being compared in the given option instead of DCE.

Final Answer:

A. False B. False C. True

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