10 1 AREAS OF PARALLELOGRAMS AND TRIANGLES Postulates

Postulates � The area of a square is the square of the length of

Altitude � To a base, is any segment perpendicular to the line containing the

Theorem � The area of a rectangle equals the product of its base and

Theorem � The area of a parallelogram equals the product of a base and

This green segment would also be an altitude. Notice its length is congruent to

Theorem What this theorem means as the corresponding height is the length of the

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10. 1 AREAS OF PARALLELOGRAMS AND TRIANGLES

Postulates � The area of a square is the square of the length of a side. (A = s 2) s s � If two figures are congruent, then they have the same area.

Altitude � To a base, is any segment perpendicular to the line containing the base from any point on the opposite side.

Theorem � The area of a rectangle equals the product of its base and height. � A=bh

Theorem � The area of a parallelogram equals the product of a base and the height to that base. (A=bh) 12 5

This green segment would also be an altitude. Notice its length is congruent to the other altitudes.

Find the area. 31 12 45°

Theorem What this theorem means as the corresponding height is the length of the altitude that intersects the base you are using. � In all right triangles it does not matter what the base and height are, because they are both the legs, (one leg is always the base and one leg is always the altitude). However in triangles that are not right triangles the height must be identified after you decide which segment you are going to use as your base. A lot of people struggle with determining the area for these types of triangles because they simply want to take the two values you are given as sides and multiply and divide by 2, where that only works in right triangles. SO BE CAREFUL �