Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Introduction to Euclid's Geometry, Exercise 1: Exam Practice

It is known that, if $x+y=10$, then $x+y+z=10+z$. Which Euclid's axiom is used?

Solve the equation $y-25=40$ and state which axiom will you use here?

If $A, B$ and $C$ are three collinear points, name all the line segments determined by them.

Given four collinear points $A, B, C$ and $D$. List all the line segments determined by these.

Read the following statements which are taken as axiom:

I. If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.

II. If a transversal intersects two parallel lines, then alternate interior angles are equal.

Is this system of axioms consistent? Justify your answer.

If $AB=(x+3), BC=2x$ and $AC=(4x-5)$, then for what value of $x, B$ lies on $AC$?

In the given figure, $AC$ is a perpendicular,  $\angle 2=\angle 1$ and $\angle 3=\angle 4$. Find $\angle \theta$.

If $S$ is a point lies in the interior of $\angle PQR$ such that, $\angle PQR=80°$ and $\angle PQS=35°$, determine the measure of $\angle RQS$.