2 And 3 Dimensional Figures Flashcards
What is an acute angle?
Angle that measures less than 90*
What is the common endpoint in an angle called?
The vertex
What are complementary angles?
2 angles whose sum is 90*
What is are supplementary angles?
2 angles whose sum is 180*
What are vertical angles?
They are formed when two lines intersect. The angles opposite each other are vertical angles and therefore congruent
What tools are needed to construct simple, yet accurate geometric figures by hand?
Compass and a straight edge
What are the two ways to classify a triangle?
By its congruent sides or angles
What are the three classifications of triangles based on congruent sides?
Scalene: no sides congruent
Isosceles: two sides are congruent (legs) and third side is the base
Equilateral: all sides are equal
What are the three classifications of triangles based on congruent angles?
Acute: all angles are less than 90*
Right: one right angle
Obtuse: one angle over 180*
What is a regular polygon?
Polygon that is equilateral and equiangular
What is the sum of all pairs of interior and exterior angles of polygons?
180*. They are supplementary
Describe the transformation of translation.
A figure undergoes a translation when it slides a certain distance in a certain direction. The translated figure is called the image if the original figure.
Describe the transformation of reflection?
Produces mirror image of original figure by flipping across a line.
Bilateral symmetry
A figure can be divided in half by a line of symmetry so that both sides are mirror images of each other
Describe the transformation of rotation
Image rotates around a point
Rotational symmetry
A figure can be rotated less than 360* and the object appears unchanged, ie an equilateral triangle
What is a polyhedron?
A three dimensional solid where each face is a polygon. Prisms, cubes, pyramids
What are the corners of polyhedrons called?
Vertices
What are the parts of a prism?
The congruent faces are called bases the other faces are parallelograms
What is the parallel axiom?
If two lines are intersected by a third so that the sum of the interior angles on the same side is 180*, than the lines are parallel.
If less the sum of interior angles is less than 180*, than the lines are not parallel and will intersect on the interior side
Side-angle-side (SAS) triangle congruence theorem
If two sides and the angle in between are congruent, than the triangles are congruent
Angle-side-angle (ASA) triangle congruence Theorem
If two angles and the side in between are congruent, than the triangles are congruent
Angle-angle (AA) congruence theorem
If two angles in one triangle are congruent to the same angles in another triangle, than they are similar
Isosceles Triangle Theorem
If triangle is iscosceles, than angles opposite congruent sides are congruent
Converse of the Iscosceles triangle theorem
If two angles of a triangle are congruent, than the triangle is Iscosceles and the opposite sides are congruent as well
What is a proof?
Sequence of statements, each justified by a postulate or theorem, that demonstrates a statement to be true.
