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Questions and Answers
Since $CEDF$ is a parallelogram, $DF$ is parallel to $CE$. Therefore, $\triangle BEG \sim \triangle ______$.
Since $CEDF$ is a parallelogram, $DF$ is parallel to $CE$. Therefore, $\triangle BEG \sim \triangle ______$.
DFH
Given $AE : EB = 1 : 4$, let $AE = x$ and $EB = 4x$. Then $AB = 5x$, which means $CD = ______$ because $ABCD$ is a rectangle.
Given $AE : EB = 1 : 4$, let $AE = x$ and $EB = 4x$. Then $AB = 5x$, which means $CD = ______$ because $ABCD$ is a rectangle.
5x
Since $\triangle BEG \sim \triangle DFH$, we have $\frac{BE}{DH} = \frac{4x}{DH} = \frac{BG}{FH}$. Also, $CH = CD - DH = 5x - DH$. Since $CEDF$ is a parallelogram, $CD = EF = EB + BF = 4x + BF$, which leads to $DH = ______$.
Since $\triangle BEG \sim \triangle DFH$, we have $\frac{BE}{DH} = \frac{4x}{DH} = \frac{BG}{FH}$. Also, $CH = CD - DH = 5x - DH$. Since $CEDF$ is a parallelogram, $CD = EF = EB + BF = 4x + BF$, which leads to $DH = ______$.
x
The ratio of the sides of $\triangle BEG$ and $\triangle DFH$ is $\frac{BE}{DH} = \frac{4x}{x} = 4$. Therefore, the ratio of their areas is the square of this ratio, which is $4^2 = ______$.
The ratio of the sides of $\triangle BEG$ and $\triangle DFH$ is $\frac{BE}{DH} = \frac{4x}{x} = 4$. Therefore, the ratio of their areas is the square of this ratio, which is $4^2 = ______$.
Given the area of $\triangle BEG$ is $320 cm^2$, and the ratio of areas $\frac{\triangle DFH}{\triangle BEG} = 16$, the area of $\triangle DFH$ is $16 \times 320 cm^2 = ______ cm^2$.
Given the area of $\triangle BEG$ is $320 cm^2$, and the ratio of areas $\frac{\triangle DFH}{\triangle BEG} = 16$, the area of $\triangle DFH$ is $16 \times 320 cm^2 = ______ cm^2$.
Flashcards
Parallelogram
Parallelogram
A quadrilateral with opposite sides parallel and equal in length. Its opposite angles are equal, and its diagonals bisect each other.
Rectangle
Rectangle
A quadrilateral with four right angles. Opposite sides are equal and parallel.
Similar Triangles
Similar Triangles
Triangles that have the same shape, but can be different sizes. Their corresponding angles are equal and corresponding sides are in proportion.
Scale Factor
Scale Factor
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Area of a Triangle
Area of a Triangle
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Study Notes
- Given rectangle ABCD
- E is a point on AB
- Ratio of AE:EB = 1:4
- CEDF is a parallelogram
- BF intersects CE at G
- BF intersects CD at H
- Area of triangle BEG is 320 cm²
- Need to find the area of triangle DFH
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