Karnataka Board Solutions for Chapter: Solved Examples, Exercise 1: Exercise 1

In Fig identify:

Three linear pairs.

In Fig identify:

Two pairs of vertically opposite angles.

Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by using SAS congruence rule. If the triangles are congruent, write them in symbolic form.

                        $∆ABC$                                          $∆DEF$

(b) $AB=4.5 \mathrm{cm}, AC=4 \mathrm{cm}, \angle A=60° DE=4 \mathrm{cm}, FD=4.5 \mathrm{cm}, \angle D=55°$

Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by using SAS congruence rule. If the triangles are congruent, write them in symbolic form.

                        $∆ABC$                                          $∆DEF$

$BC=6 \mathrm{cm}, AC=4 \mathrm{cm},\angle B=35° DF=4 \mathrm{cm}, EF=6 \mathrm{cm}, \angle E=35°$

$AB=AC$ and $AD$ is the bisector of $\angle BAC$.
Is $\Delta ADB\cong \Delta ADC$? Give reasons.

$AB=AC$ and $AD$ is the bisector of $\angle BAC$.

Is $\angle B=\angle C$? Give reasons.

Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, using RHS congruence rule. In case of congruent triangles, write the result in symbolic form:

                 $∆ABC$                                                         $∆DEF$

$\angle A=90°, AC=5 \mathrm{cm}, BC=9 \mathrm{cm} \angle Q=90°, PR=8 \mathrm{cm}, PQ=5 \mathrm{cm}$

$DA\perp AB, CB\perp AB$ and $AC=BD$. State the three pairs of equal parts in $∆ABC$ and $∆DAB$. Which of the following statements is meaningful?

$∆ABC\cong ∆ABD$