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. Prove that Δ ADE ~ Δ GCF, if AB ⊥ BC, FG ⊥ BC and DE ⊥ AC.DE≅DF≅EF, so △DEF is both an isosceles and an equilateral triangle. Length of the other side = 15 + 5 = 20 cm X 2 + 5x – 300 = 0 (Dividing both sides by 2) Hypotenuse of a right triangle is 25 cm and out of the remaining two sides, one is longer than the other by 5 cm. Find the value of x, if DE || BC in Δ ABC. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Find PR, if ΔABC ~ ΔQRP, area (ΔABC) / area (ΔPQR) = 9/4, AB = 18 cm and BC = 15 cm. The corresponding sides of two similar triangles are proportional. Length of the shadow of the tower, L 2= 28 m Let the height of the tower be ‘x' metres.
A vertical pole of length 6 metre casts a shadow 4 metre long on the ground and at the same time a tower casts a shadow 28 metre long. From the above triangle ABC, we can see that.Īgain applying Basic Proportionality Theorem, With the help of the following figure prove that BF/FE = BE/EC.
Perpendicular is the side next to 90 ° angle.
Hypotenuse is the side opposite to the right angle.One angle of all the angles is greater than 90 degrees.All the angles are less than 90 degrees.The angle bisector form the symmetry line of an equilateral triangle.Median, altitude, angle bisector, perpendicular bisector lie at one line.Chords are the sides of the circumcentre.Circumcentre lies inside its triangle if all three angles are acute.Third unequal angle is an acute or obtuse.A congruent angle is an angle opposite to the equal sides.The angles opposite to the equal sides of an isosceles triangle are equal.Each angle on a scalene triangle is half that of its opposite side when inscribed in a circle.Cannot be bisected into two equal halves.The longest side is the one which is opposite to the longest angle.The smallest side is one which is opposite to the smallest angle.Refer to the table below for the types of triangles and their properties. Orthocentre: A triangle's orthocentre is the intersection of the perpendiculars drawn from its vertices to its opposite sides. The extended base of the altitude is found where it crosses the altitude. It divides each of the medians in the ratio 2:1, which means it is located at 13% of the distance between each side.Īltitude: A triangle’s altitude is formed by a line segment that crosses through its vertex and is perpendicular to the line containing its base.
Median: A median is the line segment connecting the vertex of the triangle to the midpoint of the opposite side of the triangle.Īngle Bisector: An angle bisector is also defined as the angle in an equilateral triangle or the non-congruent angle in an isosceles triangle.Ĭentroid: An intersection of a triangle’s medians (the lines connecting its vertex to its opposite vertex) is a triangle’s centroid.
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