Question 513 Marks
Prove that the bisectors of the base angles of an isosceles triangle are equal.
Answer
View full question & answer→self
Questions · Page 2 of 2
[3 marks sum]
Question 523 Marks
In the given figure, $AD = AE$ and $\angle BAD =\angle CAE$. Prove that: $AB = AC$.
Answer
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Question 533 Marks
In the given figure, $AB \| CD$ and $CA = CE$. Find the values of $x, y$ and $z$.
Answer
View full question & answer→$x=36, y=68, z=44$
Question 543 Marks
In the given figure, $BD \| CE ; AC = BC , \angle ABD =20^{\circ}$ and $\angle ECF =70^{\circ}$. Find $\angle GAC$.
Answer
View full question & answer→$130^{\circ}$
Question 553 Marks
In each of the following figures, find the value of $x$ :
Answer
View full question & answer→(i) $x=110$
(ii) $x=55$
(iii) $x=20$
(ii) $x=55$
(iii) $x=20$
Question 563 Marks
(Converse of Theorem 1) : If two angles of a triangle are equal, then the sides opposite to them are also equal.
Given: $\quad A \triangle ABC$ in which $\angle B =\angle C$.
To prove : $\quad AB = AC$.
Construction : From A , draw $AD \perp BC$.
Proof.
Given: $\quad A \triangle ABC$ in which $\angle B =\angle C$.
To prove : $\quad AB = AC$.
Construction : From A , draw $AD \perp BC$.
Proof.
Answer
View full question & answer→| Statement | Reason |
| 1. In $\triangle A B D$ and $\triangle A C D$, we have : (i) $\angle ABD =\angle ACD$ (ii) $\angle ADB =\angle ADC$ (iii) $AD = AD$ | Given. Each $=90^{\circ}$, since $AD \perp BC$ (by construction) Common. AAS-axiom of congruency. c.p.c.t. |
| 2. $\triangle ABD \cong \triangle ACD$ | |
| 3. $AB = AC$ Hence, $\angle B =\angle C \Rightarrow AB = AC$. |
Question 573 Marks
Answer
View full question & answer→| Statement | Reason |
| 1. In $\triangle A B D$ and $\triangle A C D$, we have : (i) $AB = AC$ (ii) $\angle ADB =\angle ADC$ (iii) $AD = AD$ | Given. Each $=90^{\circ}$, since $AD \perp BC$ (by construction) Common. RHS-axiom of congruency. c.p.c.t. |
| 2. $\therefore \triangle ABD \cong \triangle ACD$ | |
| 3. $<br>\angle B=\angle C<br>$ Hence, $AB = AC \Rightarrow \angle B =\angle C$. |