Question
In the given figure, AB = CD and AD = CB.
Prove that :
(i) $\triangle ABD =\triangle CDB$
(ii) $\angle A =\angle C$
Prove that :
(i) $\triangle ABD =\triangle CDB$
(ii) $\angle A =\angle C$
✓
Answer
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Madan Singh runs a rental car company. He charges ₹ 250 per day plus ₹ 15 for every kilometre the car is driven. Professor Dayal rents a car for 1 day, while his own car is being repaired. He assures Madan Singh that he will pay him more than ₹ 500 as rent for the day.
Q.1. The inequality for the rent paid by Dayal for 1 day is :
(a) $3 x<100$$\quad$$\quad$ (b) $x>25$ $\quad$$\quad$(c) $3 x>50$ $\quad$$\quad$(d) $x<75$
Q.2. The solution set for the inequality obtained above is given by :
(a) $\{16,17,18, \ldots\}$ $\quad$(b) $\{17,18,19, \ldots\}$$\quad$ (c) $\{19,20,21, \ldots\}$ $\quad$(d) $\{20,21,22, \ldots\}$
Q.3. Dayal estimated that the rent for 1 day would be less than $₹ 600$ as he calculated the distance he has to drive the car. The inequality for the rent in this case would be :
(a) $y>30$ $\quad$$\quad$(b) $2 y<35$ $\quad$$\quad$(c) $3 y<70$ $\quad$$\quad$(d) $4 y>45$
Q.4. The solution set for the above inequality is given by :
(a) $\{\ldots ., 20,21,22,23\}$ $\quad$$\quad$(b) $\{\ldots ., 17,18,19,20\}$
(c) $\{\ldots ., 18,19,20,21\}$ $\quad$$\quad$(d) $\{\ldots ., 15,16,17,18\}$
→Q.1. The inequality for the rent paid by Dayal for 1 day is :
(a) $3 x<100$$\quad$$\quad$ (b) $x>25$ $\quad$$\quad$(c) $3 x>50$ $\quad$$\quad$(d) $x<75$
Q.2. The solution set for the inequality obtained above is given by :
(a) $\{16,17,18, \ldots\}$ $\quad$(b) $\{17,18,19, \ldots\}$$\quad$ (c) $\{19,20,21, \ldots\}$ $\quad$(d) $\{20,21,22, \ldots\}$
Q.3. Dayal estimated that the rent for 1 day would be less than $₹ 600$ as he calculated the distance he has to drive the car. The inequality for the rent in this case would be :
(a) $y>30$ $\quad$$\quad$(b) $2 y<35$ $\quad$$\quad$(c) $3 y<70$ $\quad$$\quad$(d) $4 y>45$
Q.4. The solution set for the above inequality is given by :
(a) $\{\ldots ., 20,21,22,23\}$ $\quad$$\quad$(b) $\{\ldots ., 17,18,19,20\}$
(c) $\{\ldots ., 18,19,20,21\}$ $\quad$$\quad$(d) $\{\ldots ., 15,16,17,18\}$
Let $\mathrm{U}=\{1,2,3,4,5,6,7,8,9,10\}$ be the universal set and let $A=\{2,3,4,5,6\}$ and $B=\{3,5,7,8\}$ be its subsets.
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Verify that: (v) $(\mathrm{A} \cup \mathrm{B})^{\prime}=\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$, (vi) $(\mathrm{A} \cap \mathrm{B})^{\prime}=\left(\mathrm{A}^{\prime} \cup \mathrm{B}^{\prime}\right)$
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Verify that: (v) $(\mathrm{A} \cup \mathrm{B})^{\prime}=\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$, (vi) $(\mathrm{A} \cap \mathrm{B})^{\prime}=\left(\mathrm{A}^{\prime} \cup \mathrm{B}^{\prime}\right)$
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(i) $\triangle AOD \cong \triangle BOC$
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(iii) $\angle ADB =\angle ACB$
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→(i) $\triangle AOD \cong \triangle BOC$
(ii) $A D=B C$
(iii) $\angle ADB =\angle ACB$
(iv) $\triangle ADB \cong \triangle BCA$
In the given figure, $\triangle ABC$ is an equilateral triangle whose side BC has been produced in both the directions to D and E respectively. Prove that $\angle ACD =\angle ABE$.
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