Question

all the theorems related to chapter triangles for class 10

Answer 1

$\huge\color{red}{HEY \: DEAR}$

⭐️ THEOREM 1 : The area of triangular regions being on the same base and between same parallels is equal.

⭐️ THEOREM 2 : The perpendicular bisectors of sides of a triangle are concurrent.

⭐️ THEOREM 3 : The perpendiculars from vertices of triangle on the opposite sides are concurrent.

⭐️ THEOREM 4 : The internal bisectors of angles of a triangle are concurrent.

⭐️ THEOREM 5 : The three medians of a triangle are concurrent.


⭐️ THEOREM 6 : The line segment joining the midpoints of two sides of a tfiange is parallel to the third side and equal to half of it.

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Answer 2

Hey dear ❤️❤️☺️

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$\bthll{Triangle Similarity of Triangles Theorem}$

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THEOREM 1:

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️

THEOREM 2:

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️


THEOREM 3:

If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar. This is also called AAA (Angle-Angle-Angle) criterion....



✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️


THEOREM 4:

If in two triangles, sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar. This is also called SSS (Side-Side-Side) criterion.

✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️


THEOREM 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. This is also called SAS (Side-Angle-Side) criterion.


✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️


THEOREM 6:

The ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️

THEOREM 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.

✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️

THEOREM 8:

Pythagoras Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️





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Høpé.. ÎtS hĺp űh... (^_-)❤️
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$Sumit Tiwari from Azamgarh [UP]$