How do you prove the area of Triangle A is congruent to Triangle B in this trapezoidAttachment 21679?

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- Jun 16th 2011, 08:25 PMAquameatwadArea of Triangles in Trapezoid
How do you prove the area of Triangle A is congruent to Triangle B in this trapezoidAttachment 21679?

- Jun 16th 2011, 08:27 PMProve ItRe: Area of Triangles in Trapezoid
- Jun 16th 2011, 08:30 PMAquameatwadRe: Area of Triangles in Trapezoid
No i don't have lengths. It is supposed to apply to any trapezoid. Now i found this link Trapezoid -- from Wolfram MathWorld which gives formulas as to why the areas are equal. But i don't understand why.

- Jun 16th 2011, 10:11 PMBAdhiRe: Area of Triangles in Trapezoid
- Jun 17th 2011, 04:32 AMAquameatwadRe: Area of Triangles in Trapezoid
You are right badhi. So i guess the question is why do they have the same area?

- Jun 17th 2011, 05:01 AMSorobanRe: Area of Triangles in Trapezoid
Hello, Aquameatwad!

Quote:

How do you prove the area of Triangle A is equal to Triangle B in this trapezoid?

Code:`P Q`

- *-------*

: * * * *

: * A * * B *

: * * * *

h * * * *

: * * C * *

: * * * *

: ** **

- *-------------------------------*

S R

$\displaystyle \Delta PSR\text{ and }\Delta QSR\text{ have the same base (SR) and the same height (h).}$

$\displaystyle \text{Hence: }\:\text{area}(\Delta PSR) \;=\;\text{area}(\Delta QSR)$

. . . . . . . . . . $\displaystyle A + C \;=\;B + C$

$\displaystyle \text{Therefore: }\qquad\quad\; A \;=\;B$

- Jun 17th 2011, 05:18 AMAquameatwadRe: Area of Triangles in Trapezoid
Wow Soroban its that simple? I was trying to prove it by somehow by showing Triangle C was congruent to the Triangle with base PQ ( i guess we can call it D). which it is. Could i have used this information to prove A=B?