...in practice it is much more easily accomplished. The following geometrical theorems must be known: (1) The angles at the base of an isosceles triangle are equal. (2) The three angles of a triangle are together equal to two right angles. (3) The angle at the centre...

...2, 8, 4. 1. Define an angle, a right angle, a semi-circle and an isosceles triangle. 2. The angles at the base of an isosceles triangle are equal to each other ; and if the equal sides be produced, the angles on the other side of the base are also equal. 8. If...

...PROPOSITIONS 1—26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS PKOPOSITION V. The angles at the base of an isosceles triangle are equal to each other; and if the equal sides be produced, the angles on the other side of the base shall be equal. Let be...

...triangle? A rhombus? A rectangle? A segment of a circle? Draw a figure of each. 2. Prove that the angles at the base of an isosceles triangle are equal to each other. 3. Prove that straight lines which are parallel to the same straight line are parallel to each other....

...when we take for granted any principle which requires proof. In proving, for example, that the angles at the base of an isosceles triangle are equal to each other, if we assume that the angles on the other side of the base are equal to each other, we should take...

...a greater angle. For Admission as Pupil-Teacher of the Fourth Class. (One hour and a-half allowed.) 1. The angles at the base of an isosceles triangle are equal to one another. [Let DEF be the triangle, and use the following construction : — In DE take any point...

...other then the angles which are opposite to the equal sides are equal to each other. [or, The angles at the base of an isosceles triangle are equal to each other. ,] Let ABC represent a triangle in which the side AB is equal to the side AC ; it is required to prove...

...propositions in which two triangles are proved equal in all respects. (b) State the converse of the following: 1. The angles at the base of an isosceles triangle are equal. '2. Triangles on the same base and between the same parallels are equal in area. 10. In the triangle...

...vertex angle. An equilateral triangle is one whose three sides are equal. PROPOSITION XVIII. THEOREM 7 1. The angles at the base of an isosceles triangle are equal. A B GIVEN — the isosceles triangle ABC, AB and AC being equal sides. To PROVE the angle B equals...

...vertex angle. An equilateral triangle is one whose three sides are equal. PROPOSITION XVIII. THEOREM 7 1. The angles at the base of an isosceles triangle are equal. B GIVEN — the isosceles triangle ABC, AB and AC being equal sides. To PROVE the angle B equals the...