Good Day
Everyone
Let’s have a recap
Pick Me Up
Instruction.
The class will be divided into groups There will
be words that are placed on the floor indicating
the name of geometric shapes then you just
have to get the correct shape base on what is
asking.
USING DISTANCE
FORMULA IN PROVING
GEOMETRIC PROPERTIES
Learning Objective:
At the end of the discussion, the student
should be able to:
a. define what is geometric shapes;
b. identify the properties of some geometric
shapes; and
c. prove geometric properties using the
distance formula.
Place Me Where I Belong
Instruction.
The previous names from our activity will be
your guide, where will you put the shapes and its
property.
Isosceles Triangle
- Two equal sides
- The two angles opposite to
the equal sides are equal.
Rectangle
- Has four sides and four vertices
- Opposite sides are equal
- Opposite side are parallel
- All four angles are right angle
Parallelogram
Parallelogram
- Opposite sides are equal.
- Opposite sides are parallel
- Opposite angles are equal
- Diagonals bisect each other
Right Triangle
- One angle is always 90 degrees or right
angle
- The side opposite angle of 90 degrees is
the hypotenuse.
- The hypotenuse is always the longest side.
Isosceles Trapezoid
- Has pair of parallel and unequal opposite side
(base)
- Has one pair of congruent non-parallel side
(legs)
- Lower base angles and upper base angles are
congruent
Rhombus
- All sides are equal in length
- Opposite angles are equal
- The diagonals bisect each other at 90
degrees
- Opposite sides are parallel
Square
- All four interior angle are equal to 90
degree
- All four sides are congruent or equal to
each other
- The opposite side of the square are parallel
to each other.
Geometric Shapes
Geometric shape is a flat area
surrounded by edges or an outline.
Geometric shape are precise and
regular, like squares, rectangles,
and triangles.
To prove geometric properties using the method of
coordinate geometry, consider the following guidelines
for placing figures on a coordinate plane.
1.Use the origin as the vertex or center of a figure.
2.Place at least one side of a polygon on an axis.
3.If possible, keep the figure within the first quadrant.
4.Use coordinates that make computation simple and
easy. Sometimes, using coordinates that are
multiples of two would make the computation
easier.
Example 1.
Prove that a triangle with
vertices A(1,2), B(4,6), and
C(7,2) is an isosceles triangle.
Example 2.
Prove that a quadrilateral
with vertices T(1,1), E(4,5),
N(7,5), and S(4,1) is a
parallelogram.
Example 2.
Since the opposite sides TE and NS
have equal lengths, and the opposite sides EN
and ST have equal lengths, the quadrilateral
TENS is a parallelogram.
Please count 1-4 up to the last person to
know what problem will you answer in your
notebook. All who got number one and three
will answer problem number 1 and those
who got number 2 and 4 will answer no. 2
Let’s prove the following problem.
1. Consider a square 2. Rhombus LOVE has
with vertices at M(-3,- coordinates L(-5,-2), O(-
3), N(-3, 1), H(1,1), and 2,2), V(2,4) and E(-1, -5).
S(1,-3). Prove that the Show that the diagonal
diagonals of the square of Rhombus LOVE is
are perpendicular to congruent.
each other.
Let’s prove the following problem.
1. Prove that the 2. Given the points
diagonals of sqaure P(3,2), Q(7,2), R(7,6),
ABCD is a congruent. and S(3,6), prove that
The coordinates of the the quadrilateral PQRS
vertices are A(2,4), is a square using the
B(6,4), C(6,8), and distance formula.
D(2,8).
Activity 1: Prove me
3. Prove that triangle ABC 4. Prove that the diagonals
is an isosceles triangle of the parallelogram ABCD
using distance formula. are congruent using the
The coordinates of the distance formula. The
vertices are A(1,3), B(5,3), coordinates of the vertices
and C(3,7). Show all your are A(2,3), B(6,3), C(8,7),
work and provide a clear and D(4,7). Show all your
explanation work and provide a clear
explanation.
Assignment
Read and study about the General Equation of a circle.
On your notebook answer the questions.
1. What is the standard form of the equation of a
circle?
2. How about if it is in the origin? And if it is not on the
origin?
