Lines
A series of points that extends in opposite directions without end.
What is a line?
Two angles formed by intersecting lines.
What are opposite angles?
A triangle whose angles each measure less than 90 degrees.
What is an acute triangle?
A polygon with four sides.
What is a quadrilateral?
What is a vertex?
the intersection point of two sides of a plane figure
A flat surface with no thickness. It extends in all directions with no end.
What is a plane?
Two angles that share a vertex and a common side (they are next to each other.)
What are adjacent angles?
A triangle with at least two congruent sides.
What is an isosceles triangle?
How many sides does a hexagon have?
What is 6?
What is a circle?
the set of all points in a plane that are a given distance from the center
a. A section that has two endpoints. b. A section that has one endpoint.
a.What is a line segment? b. What is a ray?
Pairs of angles which lie on the same side of a transversal and are in the 'same position'.
What are corresponding angles?
A triangle with no congruent sides.
What is a scalene triangle?
A quadrilateral which has exactly one pair of parallel sides.
What is a trapezoid?
What is a hypotenuse?
the side opposite from the right angle
a. Lines that intersect at right angles. b. The intersection if two lines intersect.
a. What are perpendicular lines? b. What is point of intersection?
a. Two angles whose sum is 90 degrees. b. Two angles whose sum is 180 degrees.
a. What are complementary angles? b. What are supplementary angles?
A segment that connects a vertex of the triangle and the midpoint of the opposite side.
What is median (bisector)?
How many degrees do the interior angles of an octagon add to?
What is 1080 degrees?
What is an angle bisector?
a ray that divides an angle into two congruent adjacent angles
a. Lines that do not lie in the same plane and do not intersect. b. Two lines that lie in the same plane and do not intersect.
a. What are skew lines? b. What are parallel lines?
a. A pair of angles which lie on opposite sides of the transversal on the interior of a pair of lines. b. A pair of angles which lie on opposite sides of the transversal on the exterior of a pair of lines.
a. What are alternate interior angles? b. What are alternate exterior angles?
Prove that the sum of the angles of a triangle is 180 degrees.
Lets take a triangle △ABC.
Consider base BC, draw a line MN, parallel to BC.
Now, AB & AC will out as transversals.
AB is transversal, and MN∥BC
⇒∠2=∠4 [Since, alternate interior angles]--(1)
AC is transversal, and MN∥BC
⇒∠3=∠5 [Since, alternate interior angles]--(2)
Adding equation(i) and (ii), we get
∠2+∠3=∠4+∠5
Adding ∠1 on both sides, we get
⇒∠1+∠2+∠3=∠1+∠4+∠5.....(iii)
Since, ∠4+∠1+∠5 will form a linear pair.
As we know that the some of angles of a linear pair is 180∘
⇒∠4+∠1+∠5=180∘
Substitute above equation in equation(iii), we get
⇒∠2+∠1+∠3=180∘
i.e., in △ABC, ∠A+∠B+∠C=180∘
What is the measure of each angle of a regular heptagon?
What is 128,57 degrees?
What is geometry?
The study of geometric figures in two dimensions (plane geometry) and three dimensions (solid geometry). It includes the study of points, lines, triangles, quadrilaterals, other polygons, circles, spheres, cubes, cuboids, prisms, pyramids, cones, cylinders, and polyhedra. Geometry typically includes the study of axioms, theorems, and two-column proofs.
Among the various types of geometry are analytic geometry, Euclidean geometry, and non-Euclidean geometry.