a The two sides are congruent if they have the same length. When we look at the figure we notice that there is a marking on CA and AF.
These markings tells us that the sides are congruent, which means the statement is true.
CA≅ AF ✓
b If points are collinear, they all lie on the same line. Examining the diagram, we see that C, A and F all lie on CF.
This means the given statement is true.
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Points C, A, and F are collinear & ✓
c Let's first mark the given angles in our diagram.
Neither ∠ CAD nor ∠ EAF are defined in such a way that we can tell if they have the same measure. Therefore, it cannot be determined if the two angles are congruent. Note that they could be congruent, but we cannot tell for sure.
∠ CAD ? ≅ ∠ EAF
d In Part A, we concluded that CA and AF are congruent because there were markings on these sides telling us they were. However, there is no such information for BA and AE.
Therefore it cannot be determined if the sides are congruent. Note that they could be congruent, but we cannot tell for sure.
BA ? ≅ AE
e For the two lines and the ray to intersect at A, we must be able to tell for sure that all of them pass through A. Since A lies on all three lines, we can say that they cross at A.
Therefore, the given statement is true.
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CF, BE, and AD intersect at pointA & ✓
f We are asked if ∠ BAC and ∠ CAD are complementary. From the figure we can tell that ∠ BAD is a right angle, since the angle is marked with a square.
The side CA is in the interior of ∠ BAD. This means that the sum of m∠ BAC and m∠ CAD must be 90^(∘). Therefore, it is true that the two angles are complementary angles.
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∠ BAC and ∠ CAD are complementary angles & ✓
g Notice that ∠ BAD and ∠ DAE form a linear pair. Since ∠ BAD is a right angle, ∠ DAE must also be a right angle.
Therefore, the given statement is true.
∠ DAE is a right angle ✓
