Prove the Thales theorem...with diagram
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Thales theorem is also known as Basic Proportionality Theorem.
It states that If a line is drawn in one side of a triangle to intersect the other two sides at distinct points, then the other two sides are divided in the same ratio.
In a triangle ABC a line DE is drawn parallel to BC.
In the figure
In triangle ADE,
the area is 1/2×AD×EN.---------> 1
In triangle BDE,
the area is 1/2×DB×EN ----------->2
so area of ADE/area of BDE= AD/DB.
In triangle ADE
area is 1/2×AE×DM
In triangle DEC,
area is 1/2×EC×DM.
area of ADE/area of DEC= AE/EC.
Since triangles BDE and DEC lie on the same base and between same parallels
AD/DB=AE/EC.
HOPE IT HELPS YOU... ☆☆
It states that If a line is drawn in one side of a triangle to intersect the other two sides at distinct points, then the other two sides are divided in the same ratio.
In a triangle ABC a line DE is drawn parallel to BC.
In the figure
In triangle ADE,
the area is 1/2×AD×EN.---------> 1
In triangle BDE,
the area is 1/2×DB×EN ----------->2
so area of ADE/area of BDE= AD/DB.
In triangle ADE
area is 1/2×AE×DM
In triangle DEC,
area is 1/2×EC×DM.
area of ADE/area of DEC= AE/EC.
Since triangles BDE and DEC lie on the same base and between same parallels
AD/DB=AE/EC.
HOPE IT HELPS YOU... ☆☆
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