O All the angles of an equilateral triangle are equal.Ĭan you notice the relation between the sides and the angles? O The two angles opposite the two equal sides of an isosceles triangle are equal. O None of the angles of a scalene triangle are equal. No.Can you tell why can’t a right-angled triangle be an equilateral triangle? The summation of the three sides helps us figure out the perimeter of the triangle.Īakash Educational Services Limited Registered office Address:.There are several ways to determine the area of an isosceles triangle, but the simplest way is ½ x base x height.This altitude from the apex angle is also responsible for dividing the isosceles triangle into two right-angled triangles that are congruent to each other. This altitude splits the apex angle into identical angles too. The perpendicular drawn from the apex angle of an isosceles triangle bisects the base into two halves.The left-out angle, which is opposite to the base, is known as the apex angle.This is also termed the isosceles triangle base angle theorem Because the base contains two congruent base angles, the angles opposite to the equal sides are congruent, respectively.The base of an isosceles triangle is the third side that is unequal to the other two sides.Two sides of an isosceles triangle (sides opposite to each other) are congruent to each other.Properties of an Isosceles Triangle.īelow are listed all the important properties related to an isosceles triangle. Therefore, side QP is congruent to side PR, which proves the theorem. Hence, due to the Angle Side Angle congruence rule, the triangles POQ and POR are congruent to each other.
Properties of isosceles triangles pro#
Angle PQO is also equal to angle PRO (angles of an isosceles triangle). Since the base is split into two halves, QO = OR. We can see that angle POQ and POR are 90 degrees in value (due to the perpendicular PO). Therefore, let us mark the point where the perpendicular bisects the base QR as O.
In an isosceles triangle, any perpendicular drawn from the vertex opposite to the base bisects the base. We can prove this by drawing a perpendicular from vertex P. Therefore, we can conclude that ∠PQR = ∠PRQ and PQ = PR in the figure given above. The Converse of the theorem is also true, which states that two sides of an isosceles triangle are congruent if the corresponding angles opposite to those lengths are equal or congruent. Suppose we have a triangle PQR which is an isosceles triangle the isosceles triangle theorem states that the angles opposite to two equal sides are equal and congruent if those lengths (sides) of a triangle are also congruent. Let us learn about the triangle in detail as we unravel its properties. The main purpose of this article is to define various properties of the isosceles triangle. Isosceles triangle: This is a special type of triangle that contains two equal sides facing opposite to each other, and the third side can be of any length.
Scalene triangle: These triangles have all sides of distinct lengths.Equilateral triangle: As the name suggests, such triangles have all three lengths identical to each other.Based on the sides, the triangle is divided into three types: Equilateral triangle, Isosceles triangle, and scalene triangle. NCERT Solutions for Class 10 Social ScienceĪ 2D figure having three sides in the cartesian plane is known as a trigon or popularly known as a triangle.NCERT Solutions for Class 9 Social Science.NCERT Solutions for Class 8 Social Science.NCERT Solutions for Class 7 Social Science.NCERT Solutions for Class 6 Social Science.JEE Advanced Previous Year Question Papers.Agra,ahmedabad,ajmer,akola,aligarh,ambala,amravati,amritsar,aurangabad,ayodhya,bangalore,bareilly,bathinda,bhagalpur,bhilai,bhiwani,bhopal,bhubaneswar,bikaner,bilaspur,bokaro,chandigarh,chennai,coimbatore,cuttack,dehradun,delhi ncr,dhanbad,dibrugarh,durgapur,faridabad,ferozpur,gandhinagar,gaya,ghaziabad,goa,gorakhpur,greater noida,gurugram,guwahati,gwalior,haldwani,haridwar,hisar,hyderabad,indore,jabalpur,jaipur,jalandhar,jammu,jamshedpur,jhansi,jodhpur,jorhat,kaithal,kanpur,karimnagar,karnal,kashipur,khammam,kharagpur,kochi,kolhapur,kolkata,kota,kottayam,kozhikode,kurnool,kurukshetra,latur,lucknow,ludhiana,madurai,mangaluru,mathura,meerut,moradabad,mumbai,muzaffarpur,mysore,nagpur,nanded,narnaul,nashik,nellore,noida,palwal,panchkula,panipat,pathankot,patiala,patna,prayagraj,puducherry,pune,raipur,rajahmundry,ranchi,rewa,rewari,rohtak,rudrapur,saharanpur,salem,secunderabad,silchar,siliguri,sirsa,solapur,sri-ganganagar,srinagar,surat,thrissur,tinsukia,tiruchirapalli,tirupati,trivandrum,udaipur,udhampur,ujjain,vadodara,vapi,varanasi,vellore,vijayawada,visakhapatnam,warangal,yamuna-nagar Classroom top menu