Question

1. state the rule that determines if each triangle is congruent. if none apply, write

one\.

1. state the rule that determines if each triangle is similar. if none apply, write

one\.

Explanation:

Step1: Analyze the first set of triangles for congruence

• For the first pair of triangles (top - left), since all three sides are marked as equal, the rule is SSS (Side - Side - Side).
• For the second pair (top - middle), there is no congruence rule as the given information does not match any of SSS, SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), or HL (Hypotenuse - Leg for right - triangles).
• For the third pair (top - right), since we have a right - angle, a side, and another side (HL - Hypotenuse - Leg for right - triangles), the rule is HL.
• For the fourth pair (middle - left), we have two angles and a non - included side (AAS - Angle - Angle - Side).
• For the fifth pair (middle - middle), we have two sides and the included angle (SAS - Side - Angle - Side).
• For the sixth pair (middle - right), since we have two angles and the included side, the rule is ASA (Angle - Side - Angle).

Step2: Analyze the first set of triangles for similarity

• For the first pair (bottom - left), \(\frac{AD}{CD}=\frac{2}{12}=\frac{1}{6}\) and \(\frac{ED}{BD}=\frac{3}{8}\), since \(\frac{AD}{CD}

eq\frac{ED}{BD}\), there is no similarity rule.

• For the second pair (bottom - middle), since \(RH\parallel IC\), by the AA (Angle - Angle) similarity criterion (corresponding angles are equal as the lines are parallel).
• For the third pair (bottom - right), \(\frac{AB}{RS}=\frac{12}{18}=\frac{2}{3}\), \(\frac{AC}{RT}=\frac{6}{9}=\frac{2}{3}\), \(\frac{BC}{TS}=\frac{8}{12}=\frac{2}{3}\), so the rule is SSS (Side - Side - Side) similarity.

Answer:

18)

• First pair: SSS
• Second pair: none
• Third pair: HL
• Fourth pair: AAS
• Fifth pair: SAS
• Sixth pair: ASA

19)

• First pair: none
• Second pair: AA
• Third pair: SSS