Flvs Geometry module 2 DBA questions

how can you prove the properties of a parallelogram?

-parallel sides are parallel -opposite sides are congruent -opposite angles are congruent -diagonals bisect each other -consecutive angles are supplementary

how can you rotate a polygon on a graph?

First Identify the coordinates of the vertices of the polygon from the given graph. Then Depending on the given degree of rotation, make the following changes to each of the vertices of the polygon. Remember, a positive rotation is counter-clockwise. And lastly Using the new locations of the vertices found in Step 2, you select the graph that correctly shows the rotated polygon.

how can you prove the midsegment of a triangle theorem?

If a segment joins the midpoints of the sides of a triangle, then the segment is parallel to the third side and the segment is half the length of the third side.

How do you prove the converse of an isosceles triangle theorem?

Isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles opposite to the congruent sides are also congruent. The proof is very quick: if we trace the bisector that meets the opposite side in point we get the the congruent angles.

What is a rigid motion? which transformations are rigid motions?

Rigid motion : a transformation that preserves length and angle measure A rigid motion is when an object is moved from one location to another and the size and shape of the object have not changed. Or a transformation that preserves length and angle measure. Rigid motion transformation: There are four types of rigid motions that we will consider: translation , rotation, reflection, and glide reflection. Translation: In a translation, everything is moved by the same amount and in the same direction.

how can you prove triangles are congruent?

The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.

how acn you prove that a point on a perpendiclaur bisector is equidistant from the endpoints of the segment it intersects?

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

how can you prove the triangle inequality theorem?

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side. In other words, this theorem specifies that the shortest distance between two distinct points is always a straight line.

how can you translate a polygon on a graph?

Translating a Polygon graphically by moving each point left, right, up, or down on the coordinate plane, or algebraically by adding or subtracting from the x- and y-coordinates of each ordered pair.

what does it mean for polygons to be congruent?(what are the requirements?)

Two polygons are congruent if their corresponding sides and angles are congruent. Note: Two sides are congruent if they have the same measure.

how can you prove the triangle sum theorem?

We can prove the triangle sum theorem by making a line passing through one of the vertices of the triangle and parallel to the opposite side. Then, we can use the parallel lines and transversal results, and the sum of angles of on a straight line property to prove the triangle sum theorem.

how can you reflect a polygon on a graph?

Well first you need to Find the coordinates of each vertex of the polygon. Then you need to Find and plot the coordinates of the vertices reflected across the x -axis. A point (a,b) reflected across the x -axis is (a,−b) . And lastly you need to Connect the reflected vertices to form the reflected polygon.

What is mapping? how can you map a figure onto itself?

mapping, is any prescribed way of assigning to each object in one set a particular object in another (or the same) set. Map figure onto itself: In order for the figure to map onto itself, the line of reflection must go through the center point.Two lines of reflection going through the sides of the figure.Two lines of reflection going through the vertices of the figure.Thus, there are four possible lines that go through the center and are lines of reflections.Therefore, the figure has four lines of symmetry.

What are the characteristics of parallelograms squares, rhombi, kites, and trapezoids?

parallelogram 1.) opposite sides are equal 2.) opposite sides are parallel 3.) opposite angles are congruent 4.) consecutive angles are supplementary 5.) diagonals bisect each other 6.) diagonals make congruent triangles Rectangle 1.) opposite sides are equal 2.) opposite sides are parallel 3.) opposite angles are congruent 4.) consecutive angles are supplementary 5.) diagonals bisect each other 6.) diagonals are congruent 7.) all 4 corner angles equal 90 degrees Rhombus 1.) opposite sides are equal 2.) opposite sides are parallel 3.) opposite angles are congruent 4.) consecutive angles are supplementary 5.) diagonals bisect each other 6.) has 4 congruent sides 7.) diagonals bisect angles 8.) diagonals are perpendicular Square 1.) opposite sides are equal 2.) opposite sides are parallel 3.) opposite angles are congruent 4.) consecutive angles are supplementary 5.) diagonals bisect each other 6.) has 4 right angles 7.) diagonals are congruent 8.) has 4 congruent sides 9.) diagonals bisect angles 10.) diagonals are perpendicular Trapezoid 1.) is a quadrilateral, not a parallelogram 2.) has one pair of parallel sides 3.) the median is parallel to the bases and equal to 1/2 the sum of the bases Kite 1.) is a quadrilateral, not a parallelogram 2.) has two sets of adjacent sides that are congruent 3.) has one set of opposite angles that are congruent 4.) diagonals are perpendicular 5.) the longer diagonal bisects the shorter diagonal (only one pair of angles bisected) 6.) two pairs of consecutive sides are congruent, but opposite sides are not congruent