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Step-4

Title:

Grade: 10-a Lesson: S2-L2

Explanation:

Description: 4

From the figure we can observe that
$d4$

ACBD is a cyclic quadrilateral and
AB is bisector of \$\angle A\$

Consider \$\triangle ABC\$ and \$\triangle ABD\$.

\begin{align} \angle CAB = \angle DAB \\ \end{align}

and

\begin{align} AC &= AD \\ \angle ACB &= \angle ADB \tag{Alternate interior angles} \\ \end{align}

So, \begin{align} \triangle ABC \cong \triangle ABD \\ \end{align}

Henced proved that \$\triangle ABC\$ and \$\cong\$ \$\triangle ABD\$ by the ASA congruence rule.

From the figure we can observe that
$d4$

Steps	Statment	Solution
1	Given	From the figure we can observe that
2	Given side of triangles	ACBD is a cyclic quadrilateral and AB is bisector of \$\angle A\$
3	Consider angles	\$\triangle ABC\$ and \$\triangle ABD\$
4	Bisects	Since AB bisects angleA , WE have
5	Angles	\$angle CAB = angle DAB\$
6	Sides	AC = AD
7	Alternate interior angles	\$angle ACB = angle ADB\$
8	Congruency	\$\triangle ABC \cong \triangle ABD\$
9	Prove that	Henced proved that \$\triangle ABC\$ and \$\cong\$ \$\triangle ABD\$ by the ASA congruence rule.

Steps

Statment

Solution

Given

From the figure we can observe that

Given side of triangles

ACBD is a cyclic quadrilateral and AB is bisector of \$\angle A\$

Consider angles

\$\triangle ABC\$ and \$\triangle ABD\$

Bisects

Since AB bisects angleA , WE have

Angles

\$angle CAB = angle DAB\$

Sides

AC = AD

Alternate interior angles

\$angle ACB = angle ADB\$

Congruency

\$\triangle ABC \cong \triangle ABD\$

Prove that

Henced proved that \$\triangle ABC\$ and \$\cong\$ \$\triangle ABD\$ by the ASA congruence rule.