Introduction to Euclid's Geometry

Things equal to the same thing are equal to one another, If equals are added to equals, the wholes are equal, The whole is greater than the part

These are three of Euclid's fundamental axioms. Option 3 is incorrect because all right angles are equal (this is actually Postulate 4). Option 5 is incorrect because Postulate 3 states a circle can be drawn with any center and any radius.

AB = CD

Given AC = BD, we can write AC = AB + BC and BD = BC + CD. Since AC = BD, we have AB + BC = BC + CD. Using Euclid's axiom 'if equals are subtracted from equals, the remainders are equal', subtracting BC from both sides gives AB = CD.

Point, Line, Plane

Point, line, and plane are taken as undefined terms in Euclid's geometry because attempting to define them leads to circular definitions. Triangle and circle can be defined using these undefined terms and other geometric concepts.

5 cm

Since R is the midpoint of PQ, it divides PQ into two equal parts. Therefore, PR = RQ = PQ/2 = 10/2 = 5 cm. This follows from the definition of a midpoint and the axiom that the whole equals the sum of its parts.