Generalizing Attributes of Similarity in Shapes(TEKS.Math.7.5.A)
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Texas 7th Grade Math › Generalizing Attributes of Similarity in Shapes(TEKS.Math.7.5.A)
Triangle ABC has sides 6, 8, 10 cm. Triangle DEF has sides 9, 12, 15 cm. Are these triangles similar?
Yes, because 6:9 = 8:12 = 10:15
No, because they are not congruent
No, because their perimeters are different
Yes, because both are triangles
Explanation
Similar figures have the same shape with corresponding sides in equal ratios. Order the sides from least to greatest to match: 6↔9, 8↔12, 10↔15. Compute ratios: 6/9=2/3, 8/12=2/3, 10/15=2/3. All corresponding ratios are equal, so the triangles are similar.
Rectangle A is 4×6 inches. Rectangle B is 10×15 inches. What is the ratio of corresponding side lengths from Rectangle A to Rectangle B?
5:2
2:5
3:5
1:1
Explanation
For similar rectangles, the ratio of corresponding sides is constant. Pair shorter to shorter and longer to longer: 4:10 = 2:5 and 6:15 = 2:5. The common ratio (scale factor from A to B) is 2:5.
Triangle GHI has sides 7, 9, 12 units. Triangle JKL has sides 14, 18, 25 units. Are these triangles similar?
Yes, because all sides are doubled
Yes, because 7:14 = 9:18 = 12:25
No, because 12:25 ≠ 1:2
Yes, because their perimeters are proportional
Explanation
To be similar, all corresponding side ratios must be equal. Match by size: 7↔14 and 9↔18 both give 1:2, but 12↔25 gives 12:25, which is not 1:2. Since one ratio is different, the triangles are not similar.
Triangle MNO has sides 5, 7.5, 10 cm. Triangle PQR has sides 6, 9, 12 cm. What is the ratio of corresponding sides from Triangle MNO to Triangle PQR?
6:5
3:4
1:1
5:6
Explanation
Identify corresponding sides by ordering lengths: 5↔6, 7.5↔9, 10↔12. Compute 5:6, 7.5:9, and 10:12. Each simplifies to 5:6, so the ratio of corresponding sides (scale factor from MNO to PQR) is 5:6.
Rectangle C is 8×12 cm. Rectangle D is 18×27 cm. Are these rectangles similar?
Yes, because 8:18 = 12:27
No, because their areas are different
Yes, because any two rectangles are always similar
No, because not all sides are equal
Explanation
Similar figures have proportional corresponding sides. Match shorter to shorter and longer to longer: 8:18 simplifies to 4:9 and 12:27 simplifies to 4:9. Since both ratios are equal, the rectangles are similar.