1. A kite is a quadrilateral with two pairs of adjacent congruent sides. Kites were historically used for rituals and are now commonly known as children's toys.
2. A kite has one set of congruent adjacent sides and one set of congruent opposite sides. If a kite's diagonals do not intersect, it is called a dart.
3. The area of a kite is half the product of its diagonals. The diagonals of a kite are perpendicular and bisect the angles between the congruent sides.
All around us, some quantities are constant and others are variable.
For instance, the number of hours in a day is constant, but the number of hours in a daylight in a day is not.
now you will explore more closely certain types of relationships between variables.
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All around us, some quantities are constant and others are variable.
For instance, the number of hours in a day is constant, but the number of hours in a daylight in a day is not.
now you will explore more closely certain types of relationships between variables.
This learner's module discusses about the topic of Radical Expressions. It also teaches about identifying the radicand and index in a radical expression. It also teaches about simplifying the radical expressions in such a way that the radicand contains no perfect nth root.
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For more instructional resources, CLICK me here! πππ
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You've seen that many quantities are related to each other. However, not all of them are directly related. Now you will explore quantities that vary inversely. In inverse variation, one quantity decreases as the other increases.
This learner's module discusses about the topic Variations. It also discusses the definition of Variation. It also discusses or explains the types of Variations. It also shows the examples of the Types of Variations.
You will learn how to get the value of a, b and c given a quadratic equations.
For more instructional resources, CLICK me here! πππ
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! πππ
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
This powerpoint presentation discusses or talks about the topic or lesson: Laws of Exponents. It also discusses and explains the rules, concepts, steps and examples of Laws of Exponents.
You've seen that many quantities are related to each other. However, not all of them are directly related. Now you will explore quantities that vary inversely. In inverse variation, one quantity decreases as the other increases.
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http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasnβt one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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2. Definition
β’KITE β is a quadrilateral with two sets of distinct
adjacent congruent sides, but opposite sides are
not congruent.
3.
4. IN ANCIENT TIME
KITE were widely considered to be
useful for ensuring a good harvest or
scaring away evil spirits.
5. IN MODERN TIME
KITE became more widely known as
children's toys and came to be used
primarily as a leisure activity
6. β’ From the definition, a kite is the only quadrilateral that we
have discussed that could be concave or non convex.
Concave or non convex kite is a kite whose diagonal do not
intersect. If a kite is concave or non convex, it is called
a dart .
8. β’ The angles between the congruent sides are called vertex
angles . The other angles are called non-vertex angles . If we
draw the diagonal through the vertex angles, we would have
two congruent triangles.
B
A C
D
9. THEOREM 1: The non-vertex angles of a kite are congruent
and the diagonal through the vertex angle is the angle
bisector for both angles.
PROOF:
GIVEN: KITE WITH πΎπΈβ ππΈ AND πΎπΌβ ππΌ
STATEMENTS REASONS
1. 1.
2. 2.
3. 3.
4. 4.
5. 5.
KITE WITH πΎπΈβ ππΈ AND πΎπΌβ ππΌ GIVEN
πΌπΈ β πΌπΈ REFLEXIVE PROPERTY
βπΎπΌπΈ β βππΌπΈ SSS CONGRUENCE POSTULATE
β πΎ β β π CPCTC
β ππΌπΈ β β πΎπΌπΈ AND β πΎπΈπΌ β β πEI CPCTC
PROVE: β πΎ β β π,
β ππΌπΈ β β πΎπΌπΈ AND β πΎπΈπΌ β β πEI
13. Example1 Continued
20
12
12
12
U
W
Z
Y
X
We can now use the formula in
finding the area of the kite.
Area of kite WXYZ=
1
2
π1π2
Area of kite WXYZ=
1
2
(ππ)(ππ)
Area of kite WXYZ=
1
2
(24)(32)
Area of kite WXYZ=384 π ππ’πππ π’πππ‘π
14. EXAMPLE 2: Given kite WXYZ
20
12
12
12
U
W
Z
Y
X
9
9
What is the length of segment XY?
15. EXAMPLE 2: Given kite WXYZ
20
12
12
12
U
W
Z
Y
X
9
9
ππ2
= ππ2
+ ππ2
ππ2
= 92
+ 122
ππ2
= 81 + 144
ππ2
= 225
XY= 15
16. Example 3
β’ Find mοG and mοJ.
60ο°132ο°
J
G
H
K
Since GHJK is a kite οG ο οJ
So 2(mοG) + 132ο° + 60ο° = 360ο°
2(mοG) =168ο°
mοG = 84ο° and mοJ = 84ο°
17. Try This!
β’ RSTU is a kite. Find mοR, mοS and mοT.
xο°
125ο°
x+30ο°
S
U
R T
x +30 + 125 + 125 + x = 360
2x + 280 = 360
2x = 80
x = 40
So mοR = 70ο°, mοT = 40ο° and mοS = 125ο°
18. QUIZ
β’ Given kite BCDA and point P be the point of
intersection of the diagonals , consider the given
information below and answer the question that
follows.
1. πΆπ΄ = 20π 2.πΆπ΄ = 14π
π΅π· = 24π π΅πΆ = 25π
What is the area of kite BCDA? π΅π =?
3. πΆπ = 5
πΆπ· = 13
π΅πΆ = 74
πΆπ΄ =?
π΅π· =?
What is the area of kite BCDA?
D
C
A
B