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1. VISHAL JHA
X-B
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2. Table of content
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3. THEOREM 6.1
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5. THEROREM 6.2
THEOREM 6.2- If a line is drawn parallel to one side of a triangle to intersect the
two other side in distinct points , the other two side are divided in the same
ratio
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6. THEOREM 6.3
Theorem 6.3-If two triangles, corresponding angles are equal , then their
corresponding sides are in the same proportion and hence the two triangles are
similar
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7. Theorem 6.4
• Theorem 6.4-If in two triangles, sides of one triangle are proportional to(i.e., in
the same ratio of ) the sides of the other triangle, then their corresponding
angles are equal and hence the two triangles are similar.
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8. Theorem 6.5
Theorem 6.5-If one angle of a triangle is equal to one angle of the other triangle
and the sides including these angles are proportional, then the two triangles are
similar
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9. Theorem 6.6
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11. 𝑎𝑟(𝐴𝐵𝐶)
𝑎𝑟(𝑃𝑄𝑅)
= 𝐴𝐵 𝑃𝑄 2 = 𝐵𝐶 𝑄𝑅 2 = 𝐶𝐴 𝑅𝑃 2
Theorem 6.7
Theorem 6.7-If a perpendicular is drawn from the vertex of the right angle of a
right triangle to the hypotenuse then triangles on both sides of the perpendicular
are similar to the whole triangle and to each other.
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12. Theorem 6.8
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14. THEOREM 6.9
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15. Now in triangle PQR , we have
PR2 = PQ2 +QR2 (PythagorasTheorem as∠𝑄 = 90° )
PR2 =AB2 + BC2 (By construction) (1)
But AC2 = AB2 +BC2 (Given) (2)
So, AC=PR [From (1)and (2)] (3)
Now In triangles ABC andPQR,
AB = PQ (By construction)
BC = QR (By construction)
AC = PR (Proved above in 3)
ABC ≅ PQR (SSS congruence )
∠𝐵 = ∠𝑄 (By CPCT)
∠𝐵 = ∠𝑄=90°
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16. THANKYOU
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