Answer:
- HU ≅ HG
- ∠R ≅ ∠F
- DE ≅ XW
Explanation:
It helps to understand what the letters in SSS, AAS, and ASA mean. S stands for side; A stands for angle. The sequence of letters refers to the sequence of sides and angles that must be shown to be congruent in order for that theorem to apply. AAS means two angles and a side not between them; ASA means two angles and the side between them.
To solve these problems, you need to identify the congruences already shown in the diagram, then find the one that is missing to finish out the sequence of sides and angles represented by the abbreviation.
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1.
Sides UF and GF are marked congruent. Side HF is congruent to itself. So to use SSS, you need the third sides of the triangles congruent:
HU ≅ HG
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2.
Side PQ is shown congruent to DQ. We know the vertical angles at Q are congruent. To use AAS, we need an angle not adjacent to the congruent sides, so we need ...
∠R ≅ ∠F
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3.
A pair of angles in each triangle is shown congruent. To use ASA, the congruent sides need to be between the congruent angles:
DE ≅ XW