In figure, if AC = BD, then prove that AB = CD.

Solution

AC = BD | Given ...(1)
AC = AB + BC
| Point B lies between A and C ...(2)
BD = BC + CD
| Point C lies between B and D ...(3)
Substituting (2) and (3) in (1), we get
AB + BC = BC + CD ⇒ AB = CD.
| Subtracting equals from equals

Some More Questions From Introduction to Euclid's Geometry Chapter

Express the following statement as a linear equation in two variables by taking present ages (in years) of father and son as x and y, respectively. Age of father 5 years ago was two years more than 7 times the age of his son at that time.

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Introduction To Euclid's Geometry

In figure, if AC = BD, then prove that AB = CD.

Some More Questions From Introduction to Euclid's Geometry Chapter

Express the following statement as a linear equation in two variables by taking present ages (in years) of father and son as x and y, respectively. Age of father 5 years ago was two years more than 7 times the age of his son at that time.

Write the equation 2x = y in the form ax + by + c = 0 and find the values of a, b, c in the equation. How many solution this equation has?

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