Flashcards on Similarity of triangles
Similarity of Triangles: Criteria, Properties & Applications
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Similarity of Triangles
18 cards
Card 1
Question: What does it mean for two triangles to be similar?
Answer: Two triangles are similar if they have the same shape but not necessarily the same size.
Card 2
Question: What are the two conditions that must be met for two triangles to be similar?
Answer: Corresponding angles are equal, and corresponding sides are proportional.
Card 3
Question: What is the constant ratio of the lengths of corresponding sides in similar triangles called?
Answer: The ratio of similarity or scale factor, often denoted by 'k'.
Card 4
Question: If ΔABC is similar to ΔDEF (ΔABC ~ ΔDEF), how do their corresponding angles relate?
Answer: ∠A = ∠D, ∠B = ∠E, and ∠C = ∠F.
Card 5
Question: If ΔABC is similar to ΔDEF (ΔABC ~ ΔDEF), how do their corresponding sides relate?
Answer: AB / DE = BC / EF = CA / FD = k (where 'k' is the ratio of similarity).
Card 6
Question: What does a scale factor 'k' greater than 1 indicate in similar triangles?
Answer: The second triangle is an enlargement of the first.
Card 7
Question: What does a scale factor 'k' between 0 and 1 (0 < k < 1) indicate in similar triangles?
Answer: The second triangle is a reduction of the first.
Card 8
Question: What special case of similarity occurs when the scale factor 'k' equals 1?
Answer: The triangles are congruent, meaning they are identical in both shape and size.
Card 9
Question: What is the AA Similarity Theorem?
Answer: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Card 10
Question: Why is checking just two angles sufficient for the AA Similarity Theorem?
Answer: Since the sum of angles in any triangle is 180°, if two pairs of angles are equal, the third pair must also be equal.