Q. 64.9( 8 Votes )
Given: ∆ABC is isosceles triangle.
To prove: ∠CAD = ∠CBE
Let ∆ABC be our isosceles triangle as shown in the figure.
We know that base angles of the isosceles triangle are equal.
Here, ∠CAB = ∠CBA ….(1)
Also here, ∠CAD and ∠CBE are exterior angles of the triangle.
So, we know that,
∠CAB +∠CAD = 180°… exterior angle theorem
And ∠CBA + ∠CBE = 180° … exterior angle theorem
So from (1) and above statement, we conclude that,
∠CAB +∠CAD = 180°
And ∠CAB +∠CBE = 180°
Which implies that,
∠CAD = 180° - ∠CAB
And ∠CBE = 180° - ∠CAB
Hence we say that ∠CAD = ∠CBE
∴For the isosceles triangle, the exterior angles so formed are equal to each other.
Rate this question :
Prove that the anRS Aggarwal & V Aggarwal - Mathematics
If the sides of aRD Sharma - Mathematics
D is any point onNCERT Mathematics Exemplar
In a triangleRD Sharma - Mathematics
In Δ ABCRD Sharma - Mathematics
In Δ PQRRD Sharma - Mathematics
<span lang="EN-USRS Aggarwal & V Aggarwal - Mathematics
Prove that the peRD Sharma - Mathematics
In Fig. 10.25, <iRD Sharma - Mathematics
In a <span lang="RD Sharma - Mathematics