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Similar Figures

Similar Figures. Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. Similar Figures. Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

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Similar Figures

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  1. Similar Figures Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

  2. Similar Figures Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. For example : the two triangles below are similar

  3. Similar Figures Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. For example : the two triangles below are similar All the angles are congruent…

  4. Similar Figures Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. For example : the two triangles below are similar All the angles are congruent… And the sides are proportional…all sides increase by a factor of 2

  5. Similar Figures Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. For example : the two triangles below are similar All the angles are congruent… And the sides are proportional…all sides increase by a factor of 2 To check or solve for unknown sides in similar triangles use a proportion.

  6. Similar Figures Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. EXAMPLE : Find the unknown side of the given similar triangles

  7. Similar Figures Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. EXAMPLE : Find the unknown side of the given similar triangles In your proportion, compare corresponding sides…

  8. Similar Figures Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. EXAMPLE : Find the unknown side of the given similar triangles

  9. Similar Figures Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. EXAMPLE : Find the unknown side of the given similar triangles Cross multiply and solve…

  10. Similar Figures Two polygons are similar if their corresponding angles are congruent and their corresponding sides are proportional. ( it’s the same as triangles )

  11. Similar Figures Two polygons are similar if their corresponding angles are congruent and their corresponding sides are proportional. ( it’s the same as triangles ) The two trapezoids below are similar figures… 6 in 9 in 8 in 8 in 12 in 12 in 10 in 15 in

  12. Similar Figures Two polygons are similar if their corresponding angles are congruent and their corresponding sides are proportional. ( it’s the same as triangles ) The two trapezoids below are similar figures… 6 in 9 in 8 in 8 in 12 in 12 in 10 in 15 in We have congruent angles and all sides have been increased by a factor of 1.5

  13. Similar Figures • In trapezoid PQRS, PQ = 12 in, QR = 5 in, RS = 15 in, and SP = 14 in. • If trapezoid TUVW is similar to trapezoid PQRS, which side lengths could be the side lengths of trapezoid TUVW? • A. TU = 24 in, UV = 15 in, VW = 30 in, WT = 42 inB. TU = 6 in, UV = 10 in, VW = 7.5 in, WT = 28 inC. TU = 6 in, UV = 15 in, VW = 7.5 in, WT = 42 inD. TU = 24 in, UV = 10 in, VW = 30 in, WT = 28 in

  14. Similar Figures • In trapezoid PQRS, PQ = 12 in, QR = 5 in, RS = 15 in, and SP = 14 in. • If trapezoid TUVW is similar to trapezoid PQRS, which side lengths could be the side lengths of trapezoid TUVW? • A. TU = 24 in, UV = 15 in, VW = 30 in, WT = 42 inB. TU = 6 in, UV = 10 in, VW = 7.5 in, WT = 28 inC. TU = 6 in, UV = 15 in, VW = 7.5 in, WT = 42 inD. TU = 24 in, UV = 10 in, VW = 30 in, WT = 28 in

  15. Similar Figures • In trapezoid PQRS, PQ = 12 in, QR = 5 in, RS = 15 in, and SP = 14 in. • If trapezoid TUVW is similar to trapezoid PQRS, which side lengths could be the side lengths of trapezoid TUVW? • A. TU = 24 in, UV = 15 in, VW = 30 in, WT = 42 inB. TU = 6 in, UV = 10 in, VW = 7.5 in, WT = 28 inC. TU = 6 in, UV = 15 in, VW = 7.5 in, WT = 42 inD. TU = 24 in, UV = 10 in, VW = 30 in, WT = 28 in As soon as you get a different answer, move to the next set

  16. Similar Figures • In trapezoid PQRS, PQ = 12 in, QR = 5 in, RS = 15 in, and SP = 14 in. • If trapezoid TUVW is similar to trapezoid PQRS, which side lengths could be the side lengths of trapezoid TUVW? • A. TU = 24 in, UV = 15 in, VW = 30 in, WT = 42 inB. TU = 6 in, UV = 10 in, VW = 7.5 in, WT = 28 inC. TU = 6 in, UV = 15 in, VW = 7.5 in, WT = 42 inD. TU = 24 in, UV = 10 in, VW = 30 in, WT = 28 in Again, different answers…

  17. Similar Figures • In trapezoid PQRS, PQ = 12 in, QR = 5 in, RS = 15 in, and SP = 14 in. • If trapezoid TUVW is similar to trapezoid PQRS, which side lengths could be the side lengths of trapezoid TUVW? • A. TU = 24 in, UV = 15 in, VW = 30 in, WT = 42 inB. TU = 6 in, UV = 10 in, VW = 7.5 in, WT = 28 inC. TU = 6 in, UV = 15 in, VW = 7.5 in, WT = 42 inD. TU = 24 in, UV = 10 in, VW = 30 in, WT = 28 in All answers are the same…

  18. Similar Figures Polygons are congruent if their corresponding sides and corresponding angles are congruent.

  19. Similar Figures Polygons are congruent if their corresponding sides and corresponding angles are congruent. EXAMPLE : Polygon PQRS is congruent to polygon TUVW. If PQ = 7 cm, QR = 21 cm, RS = 14 cm, and SP = 16 cm, what are the lengths of the sides of polygon TUVW?

  20. Similar Figures Polygons are congruent if their corresponding sides and corresponding angles are congruent. EXAMPLE : Polygon PQRS is congruent to polygon TUVW. If PQ = 7 cm, QR = 21 cm, RS = 14 cm, and SP = 16 cm, what are the lengths of the sides of polygon TUVW?

  21. Similar Figures Polygons are congruent if their corresponding sides and corresponding angles are congruent. EXAMPLE : Polygon PQRS is congruent to polygon TUVW. If PQ = 7 cm, QR = 21 cm, RS = 14 cm, and SP = 16 cm, what are the lengths of the sides of polygon TUVW?

  22. Similar Figures Three dimensional solids are similar if their corresponding side lengths, heights, or radii have equal ratios.

  23. Similar Figures Three dimensional solids are similar if their corresponding side lengths, heights, or radii have equal ratios. EXAMPLE : Is prism W similar to prism X ?

  24. Similar Figures Three dimensional solids are similar if their corresponding side lengths, heights, or radii have equal ratios. EXAMPLE : Is prism W similar to prism X ?

  25. Similar Figures Three dimensional solids are congruent if their corresponding side lengths, heights, or radii have equal measurements. Also, areas and volumes of congruent shapes and solids are equal.

  26. Similar Figures Three dimensional solids are congruent if their corresponding side lengths, heights, or radii have equal measurements. Also, areas and volumes of congruent shapes and solids are equal. Example : Is X congruent to Z ?

  27. Similar Figures Three dimensional solids are congruent if their corresponding side lengths, heights, or radii have equal measurements. Also, areas and volumes of congruent shapes and solids are equal. Example : Is X congruent to Z ? No, the corresponding lengths are not equal

  28. Similar Figures Three dimensional solids are congruent if their corresponding side lengths, heights, or radii have equal measurements. Also, areas and volumes of congruent shapes and solids are equal. Example : Is X congruent to Z ? No, the corresponding lengths are not equal EXAMPLE # 2 : If the volume of solid W = 20,000 cubic cm, what is the volume of solid Y ?

  29. Similar Figures Three dimensional solids are congruent if their corresponding side lengths, heights, or radii have equal measurements. Also, areas and volumes of congruent shapes and solids are equal. Example : Is X congruent to Z ? No, the corresponding lengths are not equal EXAMPLE # 2 : If the volume of solid W = 20,000 cubic cm, what is the volume of solid Y ? Since they are congruent solids, their volumes are equal : 20,000 cubic cm

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