Postulate1

Q. Write all the 5 Euclid's postulates with diagram

Q.

Euclid's Postulate 1 is :

1. A straight line may be drawn from any point to any other point.

2. A terminated line can be produced indefinitely.

3. All right angles are equal to one another.

4. None of these

Q. Assumptions that are specific to geometry are called ____

1. postulates
2. axioms
3. theorems
4. theory

Q.

In the figure, AC > AB and D is a point on AC such that AB = AD, then

1. BC = AD

2. BC < AD

3. BC = ¹/₂AD

4. BC > CD

Q.

In figure, C is mid-point of the segment AB, P and Q are mid-point of the segments AC and BC respectively. Prove that AP = BQ = AB/4

Q. Ram’s salary is equal to Mohan’s salary. Due to recession, the salaries of Ram and Mohan are made half. The final salary of Ram will be:

1. More than Mohan
2. Equal to Mohan
3. Same as before
4. Less than Mohan

Q. A unique line can be drawn with a minimum of two points. Which of the following postulates state this?

1. There is a unique line that passes through the given two distinct points
2. A line segment can be extended on either side to form a straight line
3. We can describe a circle with any center and radius
4. All right angles are equal

Q. In this question
In a triangle ABC , AB>AC , AD is perpendicular to BC , prove that
AB 2 ​​​​​​- AC<sup>​​​2 <sub>= BD 2= CD2
​​​​I have done it like this
In triangle ABD
AD2. = AB2 -. BD2. EQUATION 1
In triangle ADC
AD2 =. AC2 - CD2. EQUATION 2
on combining. EQUATION 1 and 2
AD2 = AB2. -. BD 2
AD2 = AC2 - CD2.
AB2 -. AC2 =. BD2 - CD2
hence proved

IS THIS CORRECT</sub></sup>

Q.

. If $a,b,c$ are the sides of a non-equilateral triangle, then the expression $(b+c–a)(c+a–b)(a+b–c)–abc$ is:

1. Negative

2. Non-negative

3. Positive

4. Non-positive

Q. A terminated line can be produced indefinitely on both the sides.

1. False
2. True

Q.

In the above question, point C is called a mid-point of line segment AB, prove that every line segment has one and only one mid-point.

Q. (i) How many lines can be drawn through a given point?
(ii) How many lines can be drawn through two given points?
(iii) At how many points can two lines at the most intersect?
(iv) If A, B and C are three collinear points, name all the line segments determined by them.

Q.

1. RHS

2. SAS

3. AAS

4. SSS

Q.
If P, Q, R are three points on a line and Q lies between P and R, then PR - PQ =

1. QR
2. PR
3. PQ
4. PQR

Q.

Euclid States That All Rights Angles Are Equal To One Another In The Form Of

1. A Proof.

2. An Axiom.

3. A Postulate.

4. A Definition.

Q. Prove that every line segment has a unique mid-point.

Q. Which of the following statements is false?
(a) Through a given point, only one straight line can be drawn.
(b) Through two given points, it is possible to draw one and only one straight line.
(c) Two straight lines can intersect at only one point.
(d) A line segment can be produced to any desired length.

Q. In fig. 3.22, seg AB $\cong$ seg PB, sec BC $\cong$ seg BQ $\angle$ABP $\cong$ $\angle$CBQ show that $△$ABC $\cong$$△$ PBQ also show seg AC $\cong$ seg PQ

Q. How many lines can be drawn through 2 distinct points?

1. 1
2. 2
3. 3
4. 4

Q. Enter the number of lines passing through a point parallel to a given line.

1. 1

Q.

How many angles are formed between two parallel lines?

1. 1

2. 2

3. 3

4. 0

Q.

The side of an equilateral triangle is given by $l$. Express its perimeter in terms of $l$.

Q. Postulates are the assumptions which are specific to geometry.

1. False
2. True

Q. Mention the Euclid's postulates. [4 MARKS]

Q. What is the least number of distinct points that determines a unique line?

1. Infinite
2. One
3. Two
4. Zero

Q. Show that if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}$then show that each ratio is $\sqrt[3]{\frac{5a^3-2c^3+4e^3}{5b^3-2d^3+4f^3}}$.

Q. Ram’s salary is equal to Mohan’s salary. Due to recession, the salaries of Ram and Mohan are made half. The final salary of Ram will be:

Q. In the adjoining figure, DE || BC. Prove that
(i) ar(∆ACD) = ar(∆ABE),
(ii) ar(∆OCE) = ar(∆OBD),

Q. In fig 5.52 In $△$PQR, Point X is the mid-point of side PQ. seg XZ || side QR, seg XY || side PR and PQ = 20 cm.

Q. How many straight lines can pass through two distinct points?

1. Two straight lines
2. Three straight lines
3. One straight line
4. Infinite straight lines