Advertisements
Advertisements
प्रश्न
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
Advertisements
उत्तर
Given in figure triangle CDE is an equilateral triangle formed on a side CD of a square ABCD.
To proof that ΔADE ≅ ∆BCE
Proof: In triangle ADE and triangle BCE,
DE = CE ...[Side of an equilateral triangle]
∠ADE = ∠BCE
∠ADC = ∠BCD = 90° and ∠EDC = ∠ECD = 60°
∠ADE = 90° + 60° = 150° and ∠BCE = 90° + 60° = 150°
AD = BC ...[Sides of a square]
∆ADE ≅ ∆BCE ...[By SAS congruence rule]
APPEARS IN
संबंधित प्रश्न
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.
In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC.
P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles
Fill the blank in the following so that the following statement is true.
In an equilateral triangle all angles are .....
Fill the blank in the following so that the following statement is true.
In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……
In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
In the given figure, the value of x is ______.
The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC = ______.
The angles of a right angled triangle are
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
