Unit 8 - Day 7

Properties of a

Unit 8 - Day 7

KITE

Property 1

Property 1

Exactly two pairs of consecutive congruent sides.

Property 1

(shorter side)
(longer side)

Property 2

One pair of opposite angles are congruent.

Property 3

Diagonals are PERPENDICULAR.
It means that they intersect at exactly 90 degrees.

lET'S WORK ON NUMBER 1 & 2

with the following idea in mind.
Remember that the sum of interior angles of a quadrilateral (any) is 360⁰. It means that the sum of the interior angles is 360⁰.

Applying property 2

no. 1

<A = 85⁰
<B = ?
<C = 43⁰
<D = ?

by property 2,
We can say that <b and <D are congruent

Fill in the Blanks

Step 1. Add the 2 given angles.

What is the sum of the 2 given angles?

Fill in the Blanks

Step 2. Subtract the sum from 360⁰.
So what is 360 - 128?

Fill in the Blanks

Property 2 states that a kite has one pair of congruent angles, which means <B and <D are equal.
Step 3. We divide the answer from STEP 2 by 2.

Multiple Choice

Property 2 states that a kite has one pair of congruent angles, which means which 2 angles are equal?

• <J & <K

• <J & <L

• <J & <M

• <K & <L

Fill in the Blanks

How to find <J?

Property 2 states that a kite has one pair of congruent angles, which means which 2 angles are equal. This means that if <L is 82, <J is equal to

.

Drag and Drop

How to find <K?



The sum of interior angles of a quadrilateral is

Placeholder

, then the we must first get the ​

Placeholder

of the 3 angles: 82 + 82 + 71

which is equal to

Placeholder

,​

Then, once we have the sum, we must now ​

Placeholder

360 and the sum which is equal to ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

245 degrees

152 degrees

360 degrees

sum

235 degrees

subtract

125 degrees

divide

Fill in the Blanks

How to find <PTQ?

Property 3 states that diagonals intersect perpendicularly.

<PTQ is an angle in the intersection of the diagonals, therefore <PTQ is equal to

.

Fill in the Blanks

How to find <PQT?

<PQT is the red angle in the figure and one of the interior angle of a triangle PQT.
Remember that the sum of the interior angle is 180, and we already have a 90⁰ and 37⁰, how many degrees is needed to get a total of a 180⁰?

Fill in the Blanks

How to find <QRT?

Property 2 states that a kite has one pair of congruent angles, which means which 2 angles are equal. This means that if <QPS is 37, <QRT is equal to

.

Fill in the Blanks

How to find <GDE?

<GDE is simply twice of the given <HDG, therefore <GDE is equal to

.

Fill in the Blanks

How to find <DEH?

<DEH is the red angle in the figure and one of the interior angle of a triangle DHE.
Remember that the sum of the interior angle is 180, and we already have a 90⁰ and 59⁰, how many degrees is needed to get a total of a 180⁰?

Fill in the Blanks

How to find <DGH?

Property 2 states that a kite has one pair of congruent angles, which means which 2 angles are equal. This means that if <DEH is 31, <DGH is equal to

.

Multiple Choice

How to find RX?

Looking at the given, we can solve it through the Pythagorean theorem. Which is the best solution based on the given? Identify carefully what exactly is RX; is it a LEG or a HYPOTENUSE?

• $$\sqrt[2]{14^2-8^2}$$

• $$\sqrt[2]{14^2+8^2}$$

Fill in the Blanks

So how long is RX?

Round off your answer up to tenths or with one decimal place only.

Multiple Choice

How to find QS?

Again, we can solve it through the Pythagorean theorem. Which is the best solution based on the given? Identify carefully what exactly is QS; is it a LEG or a HYPOTENUSE?

• $$\sqrt[2]{10^2-9^2}$$

• $$\sqrt[2]{10^2+9^2}$$

Fill in the Blanks

So how long is QS?

Round off your answer up to tenths or with one decimal place only.

Multiple Choice

How to find CD?

Again, we can solve it through the Pythagorean theorem. Which is the best solution based on the given? Identify carefully what exactly is CF; is it a LEG or a HYPOTENUSE?

• $$\sqrt[2]{23^2-15^2}$$

• $$\sqrt[2]{23^2+15^2}$$

Fill in the Blanks

Since, CD is equal with CF by Property 1,

how long is CD?

Round off your answer up to tenths or with one decimal place only.

Multiple Choice

How to solve for x?

By Property 2 of a Kite that one pair of angle is congruent. Which angles are congruent?

• <S and <T

• <S and <U

• <S and <V

Fill in the Blanks

How to solve for x?

By Property 2 of a Kite that one pair of angle is congruent. Therefore, <S and <U are equal.
Solve for x. Use Desmos.

Fill in the Blanks

How to solve for x?

The same as number 11,
by Property 2 of a Kite that one pair of angle is congruent. Therefore, < L and <N are equal.
Solve for x. Use Desmos.

Fill in the Blanks

Using the value of x, what is now the measure of <L?

Fill in the Blanks

What is the measure of the missing angle B?

Fill in the Blanks

How to find x?

Simply add all the angles equal them to 360⁰.

Use Desmos. What is x?

Fill in the Blanks

How to find <STV?

Let's solve for x first by adding the given angles equal them to 90. What is x?

Multiple Choice

How to find <STV?

Where should you use the value of x you just computed?

• 9x + 1

• 23x - 7

Fill in the Blanks

<STV is equal with <SRV by PROPERTY 2.

Therefore, what is the measure of <STV.

Keep that notes, Mr. Martinada will collect it on Monday.

Don't forget the activities due today... I'll put in the grades over the weekend. Check google classroom!