Question

1. AD = BC, BCLAE, ADIBE Perpendicular lines form right angles. 2. D and C are right angles 3 Reflexive 3. ZE = LE 1 Given 4. Triangle ADE congruent to Triangle BCE LA 5. LA = LB CPCTE

Answer 1

Given data :

AD=BC

BC is perpendicular to AE

AD is perprndicular to BE

In the given Figure,

BC is perpendicular to AE so, angle BCE =90 degree

Similarly, AD is perprndicular to BE so, angle ADE = 90 degree

And in the triangle ADE and BCE,

angle E is common in both triangles

Since, AD=BC given

So,

$\begin{gathered} \angle D=\angle C\text{ (Right angle=90)} \\ \angle E=\angle E(Common) \\ AD=BC\text{ (Given)} \\ \text{ So, by Angle Angle Side congurency property,} \\ \Delta ADE\cong\Delta BCE \end{gathered}$

From the property of congurency,(CPCT) all the corresponding sides and angles of congurent triangles are equal so,

$\angle A=\angle B\text{ (CPCT)}$