Exercise 101 Page 389

a Examining the diagram, we notice that it has two pairs of congruent sides. Also, we notice that ∠ BGI and ∠ DGO are vertical angles. By the Vertical Angles Theorem, we know that these angles are congruent.

Since we have two pairs of sides with equal lengths and the included angle is equal as well, we know by the SAS Congruence condition that the triangles are congruent.

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b Examining the diagram, we notice that the triangles have two pairs of congruent angles. Upon further inspection, we also see that the triangles share BG as a side.

Since we have two pairs of angles with equal measure and their included side is equal as well, we know by the ASA Congruence condition that the triangles are congruent.

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c Examining the diagram, we notice that the triangles have one pair of congruent angles and one pair of congruent sides. Upon further inspection, we also see that the triangles share BT as a side.

With the given information, we cannot claim congruence. The only theorem where we know two sides and an angle and where we can claim congruence, is if the angle is the side's included angle.

d Like in Part A, we can identify a vertical angle pair and by the Vertical Angles Theorem we know that these are congruent

Upon further examination, we can also identify a pair of alternate interior angles. Because IT∥ OM, we know by the Alternate Interior Angles Theorem, that they are congruent.

Since the triangles have two pairs of congruent angles and one pair of congruent sides, we can by the AAS Congruence condition claim that the triangles are congruent.

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Exercise 101 Page 389

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