∴ The man is 26 m away from the starting point. Question:A man goes 24 m towards West and then 10 m towards North. Find the length of side of the rhombus.Īnswer:∵ The diagonals of rhombus bisect each other at 90°. The length of the diagonals of a rhombus are 16 cm and 12 cm. Hence AB is the hypotenuse and ∆ABC is a right angle A. Question:In an isosceles ∆ABC, if AC = BC and AB 2 = 2AC 2, then find ∠C. Question:If triangle ABC is similar to triangle DEF such that 2AB = DE and BC = 8 cm. So, the triangle is not a right triangle. Hence, c is the hypotenuse of right triangle. (i) Let a = 7 cm, b = 24 cm and c = 25 cm. In case of a right triangle, write the length of its hypotenuse. Determine which of them are right triangles. Question:Sides of triangle are given below. ⇒ AB 2 = 2AC 2 Extra Questions for Class 10 Maths Chapter 6 Short Answer Type Question:ABC is an isosceles triangle right-angled at C. Question:Let ∆ABC ~ ∆DEF and their areas be respectively 64 cm 2 and 121 cm 2. Question:If ABC and DEF are similar triangles such that ∠A = 47° and ∠E = 63°, then the measures of ∠C = 70°. ∴ The given triangle is not a right triangle. The apothem of a regular polygon is also the height of an isosceles triangle formed by the center and a side of the polygon, as shown in the figure below.įor the regular pentagon ABCDE above, the height of isosceles triangle BCG is an apothem of the polygon.Question:Is the triangle with sides 12 cm, 16 cm and 18 cm a right triangle? Give reason.Īnswer:Here, 12 2+ 16 2 = 144 + 256 = 400 ≠ 18 2 The length of the base, called the hypotenuse of the triangle, is times the length of its leg. When the base angles of an isosceles triangle are 45°, the triangle is a special triangle called a 45°-45°-90° triangle. Base BC reflects onto itself when reflecting across the altitude.
Leg AB reflects across altitude AD to leg AC. The altitude of an isosceles triangle is also a line of symmetry. So, ∠B≅∠C, since corresponding parts of congruent triangles are also congruent. Based on this, △ADB≅△ADC by the Side-Side-Side theorem for congruent triangles since BD ≅CD, AB ≅ AC, and AD ≅AD. Using the Pythagorean Theorem where l is the length of the legs. ABC can be divided into two congruent triangles by drawing line segment AD, which is also the height of triangle ABC. Refer to triangle ABC below.ĪB ≅AC so triangle ABC is isosceles. The base angles of an isosceles triangle are the same in measure. Using the Pythagorean Theorem, we can find that the base, legs, and height of an isosceles triangle have the following relationships:
The height of an isosceles triangle is the perpendicular line segment drawn from base of the triangle to the opposing vertex. The angle opposite the base is called the vertex angle, and the angles opposite the legs are called base angles. Parts of an isosceles triangleįor an isosceles triangle with only two congruent sides, the congruent sides are called legs. DE≅DF≅EF, so △DEF is both an isosceles and an equilateral triangle.
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