A16 APPENDIX Review r h Figure 16 l 4 6 r d h w l r For a circle of radius r (diameter d r2 = ), r r d Area Circumference 2 2 π π π = = = lwh lh wh lw Volume Surface area 2 2 2 = = + + r r Volume 4 3 Surface area 4 3 2 π π = = r h r rh Volume Surface area 2 2 2 2 π π π = = + For a closed rectangular box of length l , width w , and height h , For a sphere of radius r , For a closed right circular cylinder of height h and radius r , Now Work problem 31 DEFINITION Congruent Triangles Two triangles are congruent if each pair of corresponding angles have the same measure and each pair of corresponding sides are the same length. Using Geometry Formulas A Christmas tree ornament is in the shape of a semicircle on top of a triangle. How many square centimeters cm2 ( ) of copper is required to make the ornament if the height of the triangle is 6 cm and the base is 4 cm? Solution EXAMPLE 4 See Figure 16.The amount of copper required equals the shaded area.This area is the sum of the areas of the triangle and the semicircle.The triangle has height h 6 = and base b 4. = The semicircle has diameter d 4, = so its radius is r 2. = bh r Total area Area of triangle Area of semicircle 1 2 1 2 1 2 4 6 1 2 2 12 2 18.28 cm 2 2 2 π π π = + = + = ⋅ ⋅ + ⋅ = + ≈ = = = b h r 4; 6; 2 About 18.28 cm2 of copper is required. Now Work problem 49 3 Understand Congruent Triangles and Similar Triangles Throughout the text we will make reference to triangles. We begin with a discussion of congruent triangles. According to dictionary.com, the word congruent means “coinciding exactly when superimposed.” For example, two angles are congruent if they have the same measure, and two line segments are congruent if they have the same length. In Figure 17, corresponding angles are equal and the corresponding sides are equal in length: a d, = b e, = and c f. = As a result, these triangles are congruent. In Words Two triangles are congruent if they have the same size and shape.
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