In the Fig. 5.8, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C.

Question

TextAxioms in Euclidean GeometryNCERT Exemplar

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If A, B and C are three points on a line, and B lies between A and C, then prove that AB + BC = AC.

Which of the following statements are true and which are false? Give reasons for your answers.

Euclid's Five Postulates

Consider two 'postulates' given below:

If a point C lies between two points A and B such that AC = BC, then prove that AC = ½ AB. Explain by drawing the figure.

In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

In Fig. 5.10, if AC = BD, then prove that AB = CD.