Advertisements
Advertisements
Question
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.
Advertisements
Solution
Given, X is the mid-point of AC
AX = CX = `1/2` AC
⇒ 2AX = 2CX = AC ...(i)
And Y is the mid-point of BC.
BY = CY = `1/2` BC
⇒ 2BY = 2CY = BC ...(ii)
Also, given AX = CY ...(iii)
According to Euclid’s axiom, things which are double of the same things are equal to one another.
From equation (iii), 2AX = 2CY
⇒ AC = BC ...[From equation (i) and (ii)]
APPEARS IN
RELATED QUESTIONS
Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
square
How many least number of distinct points determine a unique line?
In how many lines two distinct planes can intersect?
Euclid stated that all right angles are equal to each other in the form of ______.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AB = BC, BX = BY. Show that AX = CY.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AC = DC, CB = CE. Show that AB = DE.
Read the following statement :
An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are 60° each.
Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle.
The following statement is true or false? Give reason for your answer.
In the following figure, if AB = PQ and PQ = XY, then AB = XY.
