What is theorem 35?

If in a circle two straight lines cut one another, then the rectangle contained by the segments of the one equals the rectangle contained by the segments of the other.

What is theorem 31?

In a circle the angle in the semicircle is right, that in a greater segment less than a right angle, and that in a less segment greater than a right angle; further the angle of the greater segment is greater than a right angle, and the angle of the less segment is less than a right angle.

What is theorem 26?

26: If two triangles have two angles respectively equal to two angles and one side equal to one side, whether that at the equal angles or that subtending one of the equal angles, it will also have the remaining sides respectively equal to the remaining sides and the remaining angle to the remaining angle.

What is theorem 48?

48: If the square from one of the sides of a triangle is equal is equal to squares from the remaining two sides of the triangle, the angle enclosed by the remaining sides of the triangle is right. (general diagram)

What is theorem 36?

Theorem 36: If two sides of a triangle are unequal, then the measures of the angles opposite these sides are unequal, and the greater angle is opposite the greater side.

Theorem 35 | Theorems related to angles in a circle | Madhyamik maths chapter 7 |

What is theorem 30?

The theorem says that. : the square on the hypotenuse is equal to the sum of the squares on the other two sides.

What is theorem 28?

Theorem 28: there are infinitely many Carmichael numbers | Theorem of the week.

What is theorem 72?

Theorem 72: If an inscribed angle intercepts a semicircle, then its measure is 90°.

What is theorem 29?

29: The straight-line falling into parallel straight-lines makes the alternate angles equal to one another and the external angle equal to the angle that's internal and opposite and on the same sides and the angles that are interior and on the same sides equal to two right-angles. (general diagram)

What is theorem 19?

Theorem 19: The angle at the centre of the circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.

What is theorem 34?

34: The opposite sides and angles of parallelogram regions are equal to one another, and the diameters bisect them. (general diagram) (diagram 1) Let there be a parallelogram region, AGDB, and a diameter of it, BG.

What is theorem 32?

In any triangle, if one of the sides is produced, then the exterior angle equals the sum of the two interior and opposite angles, and the sum of the three interior angles of the triangle equals two right angles.

What is theorem 20?

Theorem 20: To investigate the angle the tangent of a circle, makes with the radius that goes through its point of contact.

What is theorem 39?

Theorem 39: If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = ( n −2) × 180°. The polygon in Figure 1 has seven sides, so using Theorem 39 gives: An exterior angle of a polygon is formed by extending only one of its sides.

What is theorem 69?

Theorem 69: The square of the measure of the hypotenuse of a right triangle is equal to the sum of the squares of the measures of the legs. ( Pythagorean theorem)

What is theorem 64?

Theorem 64: If an altitude is drawn to the hypotenuse of a right triangle, then it is the geometric mean between the segments on the hypotenuse.

What is theorem 21?

Theorem 21: If two angles of a triangle are congruent, the sides opposite the angles are congruent.

What is theorem 56?

Theorem 56 (Midpoint Theorem): The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.

What is theorem 78?

Theorem 78: In a circle, if two chords are equal in measure, then their corresponding minor arcs are equal in measure.

What is theorem 50?

Theorem 50: The sum of the measures of the. three angles of a triangle is 180º. (Triangle Sum Theorem)

What is theorem 66?

Richard Dedekind's theorem 66 states that there exists an infinite set. Its proof invokes such apparently nonmathematical notions as the “thought-world” and the self. This article discusses the content and context of Dedekind's proof.

What is theorem 45?

The 45-45-90 triangle rule states that the three sides of the triangle are in the ratio 1:1:√2. So, if the measure of the two congruent sides of such a triangle is x each, then the three sides will be x, x and √2x. This rule can be proved by applying the Pythagorean theorem.

What is theorem 60?

One of the two special right triangles is called a 30-60-90 triangle, after its three angles. 30-60-90 Theorem: If a triangle has angle measures 30 ∘ , 60 ∘ and , then the sides are in the ratio x : x 3 : 2 x . The shorter leg is always , the longer leg is always , and the hypotenuse is always .

What is theorem of 90?

The Pythagorean Theorem is one of the most important theorems in Geometry. To remind you: The Pythagorean Theorem: If one of the angles of a triangle is 90 degrees, then the square of the lengths of the two legs on either side of 90 degree angle sum to the square of the length of the side opposite the 90 degree angle.

What is theorem 23?

Theorem 23: If two angles are both supplementary and congruent, then they are right angles. Corollary to theorem 23: If two angles that form a linear pair are congruent, then they are right angles.