Elements Associated with a Triangle

Q.

$\text{In the given figure,}\Delta ABD\text{is an isosceles triangle with}AB=AD.\text{A median is drawn from}A\text{to side}BD\text{at}C.\text{Which of the following option(s) is/are correct?}$

1. $AC\text{is perpendicular to}BD$

2. $\angle BAC=\angle DAC$

3. $\Delta ABC\cong \Delta ADC$

4. $\text{Area of}\Delta ABD=\text{half of}\Delta ABC$

Q.

If $∆ABC\cong ∆PQR$and $m\angle ACB={30}^o$ then $m\angle PRQ$is

1. ${30}^o$

2. ${60}^o$

3. ${90}^o$

4. ${70}^o$

Q.

In the figure, AB = AC and AP $\perp$ BC. Then

1. AB = AP

2. AB < AP

3. AB > AP

4. AB AP

Q. In $\Delta$ABC, AD is the median. Which of these conditions should be satisfied to make $\Delta$ADB and $\Delta$ADC a similar triangles?

1. $\text{Either option B or C}$
2. $AB=AC$
3. $\angle A={90}^{\circ }$
4. $\angle B=\angle C$

Q.

FIll in the blank with the most appropriate answer.
The sum of the three sides of a triangle is greater than the sum of its three ___.

1. exterior angles
2. interior angles
3. sides
4. medians

Q.

If $\Delta ABC\cong \Delta RQP$ , then $\angle P$ = _____ .

1. $\angle A$

2. $\angle C$

3. $\angle B$

4. Both $\angle A$ and $\angle B$

Q.

In the given figure, O is the circumcentre of an equilateral triangle ABC. Here, area of $\Delta BOC=\frac{1}{3}\text{area of}\Delta ABC$.

1. True

2. False

Q. In the given figure, $\Delta ABD$ is an isosceles triangle with AB=AD. A median is drawn from A to side BD at C. Which of the following option(s) is/are correct?

1. $AC\text{is perpendicular to}BD$
2. $\angle BAC=\angle DAC$
3. $\Delta ABC\cong \Delta ADC$
4. $\text{Area of}\Delta ABD=\text{half of}\Delta ABC$

Q. Triangle ABC is right angled at A. If AB = AC, then find the measures of angle B and angle C.

1. angle B = angle C = 90°
2. angle B = angle C = 65°
3. angle B = 35° and angle C = 55°
4. angle B = angle C = 45°

Q. Line segment that connects a vertex of a triangle to the mid-point of the opposite side is known as

1. hypotunese
2. base
3. median
4. perpendicular

Q. 6cm, 7cm and 9cm can represent sides of a triangle.

1. True
2. False

Q. Are the following triangles possible?
(i) AB = 4 cm, BC = 5.6 cm, AC = 10 cm
(ii) $\angle A$ = 60${}^o$, $\angle B$ = 120${}^o$, $\angle A$ = 30${}^o$
[4 MARKS]

Q. If triangles ABC and PQR are congruent and AM and PN are the medians, then identify the correct relations.

1. AB = PQ
2. BC = QR
3. AC = PR
4. AM = PN
5. BM = MC
6. AM = PQ
7. PN = NR
8. BC = NR

Q. In an isosceles triangle ABC, AB = AC and BA is produced to D, such that AB = AD. What is the value of $\angle BCD$?

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${70}^{\circ }$