SaiBook.us Geometry

Home Course Section

Register Enroll Refer

Lesson Example Discussion Quiz: Class Homework

Step-3

Title:

Grade: 10-a Lesson: S2-L2

Explanation:

Description: 3

From the figure we can observe that

$d3$

\begin{align} AB ∥ CD \tag{Given}\\ EB = EC \tag{Given}\\ \end{align} and E is the midpoint of AD and BC

Consider \$\triangle AEB\$ and \$\triangle DEC\$.

\begin{align} EA &= ED \\ \angle AEB &= \angle DEC \tag{Alternate interior angles} \\ \angle ABE &= \angle DCE \tag{Alternate interior angles} \\ \end{align}

So, \begin{align} \triangle AEB \cong \triangle DEC \\ \end{align}

Henced proved that \$\triangle AEB\$ and \$\cong\$ \$\triangle DEC\$ by the ASA congruence rule.

From the figure we can observe that
$d3$

Steps	Statment	Solution
1	Given	From the figure we can observe that
2	Given side of triangles	AB ∥ CD and EB = EC
3	Mid point	E is the mid-point of AD and BC
4	Consider angles	\$\triangleAEB \cong \triangle DEC\$
5	side	EA = ED
6	Alternate interior angles	\$angle AEB = angle DEC\$ and \$angle ABE = angle DCE\$
7	Congruency	\$\triangle AEB \cong \triangle DEC\$
8	Prove that	Henced proved that \$\triangle AEB\$ and \$\cong\$ \$\triangle DEC\$ by the ASA congruence rule.

Steps

Statment

Solution

Given

From the figure we can observe that

Given side of triangles

AB ∥ CD and EB = EC

Mid point

E is the mid-point of AD and BC

Consider angles

\$\triangleAEB \cong \triangle DEC\$

side

EA = ED

Alternate interior angles

\$angle AEB = angle DEC\$ and \$angle ABE = angle DCE\$

Congruency

\$\triangle AEB \cong \triangle DEC\$

Prove that

Henced proved that \$\triangle AEB\$ and \$\cong\$ \$\triangle DEC\$ by the ASA congruence rule.