3.4e: Congruent and Similar Solids p GSE’s Primary Secondary M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem) M(G&M)–10–4 Applies the concepts of congruency by solving problems on or off a coordinate plane involving reflections, translations, or rotations; or solves problems using congruency involving problems within mathematics or across disciplines or contexts. M(G&M)–10–5 Applies concepts of similarity by solving problems within mathematics or across disciplines or contexts M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures) or surface area or volume of three

Similar Solids: Solid shapes with the same shape, different size The two pyramids are similar because the scale factors of each corresponding linear measurements are the same

If the scale factor is 1:1, then the solids are _______________ Congruent Determine if the solids are similar, congruent, or neither Similar Not similar

What is that scale factor of these prisms? Does it matter which set we use? These are the a:b numbers which indicates the linear ratio of the sides Use SA= Ph + 2B for both figures

Theorem 11-1: If two solids are similar with a scale factor of a:b then, Surface area’s have a ratio of Volume has a ratio of Use the theorem 11-1 to determine the ratio of the surface area’s

example The two prisms are similar. If the volume of the smaller prism is 108 inches cubed, Find the volume of the larger prism.

The ratio of the smaller prisms surface area to the larger one is 20:45. Find the ratio of the volumes.

Ex. Using the scale factor of similar solids The prisms are similar with a scale factor of 1:3. Find the surface area and volume of prism G. The surface area of prism F is 24 square feet The volume of prism F is 7 cubic feet.

1)Two rectangular prisms are similar. The measures of two corresponding sides are 1 m and 2 m. What is the ratio of the volumes of the prisms? 2) The volume of the larger prism is 108 cm 3. If the prisms are similar, what is the volume of the smaller prism? 3 cm 2 cm 3) Two cones are similar. If the ratio of the volumes is 27:125, What is the ratio of the radii?

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