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You have also learned about teiangles congruence of triangles on class 10 maths ch triangles gmbh same, where it clearly stated that two figures are said to be congruent if they have the same shape and the same size.

However, in Class 10 � Triangles chapter, you will study those figures, which have the same shape but not necessarily the same size. Towards the end of Chapter 6 � Triangles, Class 10 Solutionsyou will learn to prove several points such as � two figures having the same shape but not necessarily the same size are called similar figures; all congruent figures are similar, but the converse is not true; if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

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Note: Similar figures are congruent if there is one to one correspondence between the figures. Any two triangles are similar, if their. Statement: 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. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Note: If the areas of two similar triangles are equal, the triangles are congruent.

Statement: Prove that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Statement: Prove that, in a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. All congruent figures are similar but all similar figures are not congruent. SIMILAR POLYGONS Two polygons are said to be similar to each other, if: i their corresponding angles are equal, and ii the lengths of their corresponding sides are proportional Example: Any two line segments are similar since length are proportional Any two circles are similar since radii are proportional Any two squares are similar since corresponding angles are equal and lengths are proportional.

Question 9. Question Are the two triangles similar? Find whether XY BC or not. Find the height of the wall where the top of the ladder touches it. DF OC Proof. A vertical pole of length 8 m casts a shadow 6 cm long on the ground and at the same time a tower casts a shadow 30 m long. Find the height of tower. State whether the given pairs of triangles are similar or not. In case of similarity mention the criterion.

CP Hence Proved. ABCD is a rhombus. The diagonals of trapezium ABCD intersect each other at point o. Show that ABCD is a trapezium. ABCD is a trapezium. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. State and prove converse of Pythagoras theorem.

Proof: In rt. Solution: Proof.

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