Math / Geometry

QuestionThe duampint ahat a sheteh of a kite
SCAly
Use a ruler and compasses to construct the kite in the space b The diagonal $A B$ has been drawn for you. Leave in your construction lines.

Studdy Solution

STEP 1

What is this asking? We need to draw a kite, like one you'd fly, using a ruler and compass, given one of its diagonals and the lengths of the sides connected to one of its endpoints. Watch out! Remember, a kite isn't just any four-sided shape.
Two pairs of its sides need to be equal in length, and they're adjacent, not opposite each other!

STEP 2

1. Draw the first side
2. Draw the second side
3. Find the third point
4. Complete the kite

STEP 3

Set your compass to a width of $\text{4 cm}$ .
This matches the length of one of the sides connected to point $A$ .

STEP 4

Place the compass point on point $A$ and swing an arc intersecting the diagonal $AB$ .
This arc shows all possible locations for the endpoint of a $\text{4 cm}$ line segment starting at $A$ .

STEP 5

Now, change your compass width to $\text{5 cm}$ , the length of the other side connected to point $A$ .

STEP 6

With the compass point still on $A$ , draw another arc intersecting the diagonal $AB$ .
This arc shows all possible locations for the endpoint of a $\text{5 cm}$ line segment starting at $A$ .

STEP 7

Set your compass to $\text{4 cm}$ again, the length of one of the adjacent sides.

STEP 8

Place the compass point on point $B$ and swing an arc.
This arc represents all possible locations for the third point of the kite, which is $\text{4 cm}$ away from $B$ .

STEP 9

Set your compass to $\text{5 cm}$ , the length of the other adjacent side.

STEP 10

Keep the compass point on $B$ and swing another arc.
This arc represents all possible locations for the third point of the kite, which is $\text{5 cm}$ away from $B$ .

STEP 11

The intersection of the two arcs drawn from point $B$ gives us the location of the third point of our kite, let's call it $C$ .
This point is simultaneously $\text{4 cm}$ from $B$ and $\text{5 cm}$ from $B$ , which is exactly what we need!

STEP 12

Draw a line segment from the first intersection near $A$ (from step 2.1.2) to point $C$ .
Then, draw a line segment from the second intersection near $A$ (from step 2.2.2) to point $C$ .

STEP 13

You've now constructed the kite!
Don't erase those construction arcs – they show all the hard work you've done!

STEP 14

We've successfully drawn a kite with a diagonal of $\text{6 cm}$ and adjacent sides of $\text{4 cm}$ and $\text{5 cm}$ connected to one endpoint of the diagonal, using only a ruler and compass!

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QuestionThe duampint ahat a sheteh of a kite
SCAly
Use a ruler and compasses to construct the kite in the space b The diagonal $A B$ has been drawn for you. Leave in your construction lines.

Studdy Solution

STEP 1

STEP 2

1. Draw the first side
2. Draw the second side
3. Find the third point
4. Complete the kite

STEP 3

Set your compass to a width of $\text{4 cm}$ .
This matches the length of one of the sides connected to point $A$ .

STEP 4

Place the compass point on point $A$ and swing an arc intersecting the diagonal $AB$ .
This arc shows all possible locations for the endpoint of a $\text{4 cm}$ line segment starting at $A$ .

STEP 5

Now, change your compass width to $\text{5 cm}$ , the length of the other side connected to point $A$ .

STEP 6

With the compass point still on $A$ , draw another arc intersecting the diagonal $AB$ .
This arc shows all possible locations for the endpoint of a $\text{5 cm}$ line segment starting at $A$ .

STEP 7

Set your compass to $\text{4 cm}$ again, the length of one of the adjacent sides.

STEP 8

Place the compass point on point $B$ and swing an arc.
This arc represents all possible locations for the third point of the kite, which is $\text{4 cm}$ away from $B$ .

STEP 9

Set your compass to $\text{5 cm}$ , the length of the other adjacent side.

STEP 10

Keep the compass point on $B$ and swing another arc.
This arc represents all possible locations for the third point of the kite, which is $\text{5 cm}$ away from $B$ .

STEP 11

The intersection of the two arcs drawn from point $B$ gives us the location of the third point of our kite, let's call it $C$ .
This point is simultaneously $\text{4 cm}$ from $B$ and $\text{5 cm}$ from $B$ , which is exactly what we need!

STEP 12

Draw a line segment from the first intersection near $A$ (from step 2.1.2) to point $C$ .
Then, draw a line segment from the second intersection near $A$ (from step 2.2.2) to point $C$ .

STEP 13

You've now constructed the kite!
Don't erase those construction arcs – they show all the hard work you've done!

STEP 14

We've successfully drawn a kite with a diagonal of $\text{6 cm}$ and adjacent sides of $\text{4 cm}$ and $\text{5 cm}$ connected to one endpoint of the diagonal, using only a ruler and compass!

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QuestionThe duampint ahat a sheteh of a kiteSCAlyUse a ruler and compasses to construct the kite in the space b The diagonal ABA BAB has been drawn for you. Leave in your construction lines.

Studdy Solution

STEP 1

STEP 2

1. Draw the first side2. Draw the second side3. Find the third point4. Complete the kite

STEP 3

**Set** your compass to a width of 4 cm\text{4 cm}4 cm.This matches the length of one of the sides connected to point AAA.

STEP 4

Place the compass point on point AAA and **swing** an arc intersecting the diagonal ABABAB.This arc shows all possible locations for the endpoint of a 4 cm\text{4 cm}4 cm line segment starting at AAA.

STEP 5

Now, **change** your compass width to 5 cm\text{5 cm}5 cm, the length of the other side connected to point AAA.

STEP 6

With the compass point still on AAA, **draw** another arc intersecting the diagonal ABABAB.This arc shows all possible locations for the endpoint of a 5 cm\text{5 cm}5 cm line segment starting at AAA.

STEP 7

**Set** your compass to 4 cm\text{4 cm}4 cm again, the length of one of the adjacent sides.

STEP 8

Place the compass point on point BBB and **swing** an arc.This arc represents all possible locations for the third point of the kite, which is 4 cm\text{4 cm}4 cm away from BBB.

STEP 9

**Set** your compass to 5 cm\text{5 cm}5 cm, the length of the other adjacent side.

STEP 10

Keep the compass point on BBB and **swing** another arc.This arc represents all possible locations for the third point of the kite, which is 5 cm\text{5 cm}5 cm away from BBB.

STEP 11

The intersection of the two arcs drawn from point BBB gives us the location of the third point of our kite, let's call it CCC.This point is simultaneously 4 cm\text{4 cm}4 cm from BBB and 5 cm\text{5 cm}5 cm from BBB, which is exactly what we need!

STEP 12

**Draw** a line segment from the first intersection near AAA (from step 2.1.2) to point CCC.Then, **draw** a line segment from the second intersection near AAA (from step 2.2.2) to point CCC.

STEP 13

You've now constructed the kite!Don't erase those construction arcs – they show all the hard work you've done!

STEP 14

We've successfully drawn a kite with a diagonal of 6 cm\text{6 cm}6 cm and adjacent sides of 4 cm\text{4 cm}4 cm and 5 cm\text{5 cm}5 cm connected to one endpoint of the diagonal, using only a ruler and compass!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionThe duampint ahat a sheteh of a kite
SCAly
Use a ruler and compasses to construct the kite in the space b The diagonal $A B$ has been drawn for you. Leave in your construction lines.

1. Draw the first side
2. Draw the second side
3. Find the third point
4. Complete the kite

Set your compass to a width of $\text{4 cm}$ .
This matches the length of one of the sides connected to point $A$ .

Place the compass point on point $A$ and swing an arc intersecting the diagonal $AB$ .
This arc shows all possible locations for the endpoint of a $\text{4 cm}$ line segment starting at $A$ .

Now, change your compass width to $\text{5 cm}$ , the length of the other side connected to point $A$ .

With the compass point still on $A$ , draw another arc intersecting the diagonal $AB$ .
This arc shows all possible locations for the endpoint of a $\text{5 cm}$ line segment starting at $A$ .

Set your compass to $\text{4 cm}$ again, the length of one of the adjacent sides.

Place the compass point on point $B$ and swing an arc.
This arc represents all possible locations for the third point of the kite, which is $\text{4 cm}$ away from $B$ .

Set your compass to $\text{5 cm}$ , the length of the other adjacent side.

Keep the compass point on $B$ and swing another arc.
This arc represents all possible locations for the third point of the kite, which is $\text{5 cm}$ away from $B$ .

The intersection of the two arcs drawn from point $B$ gives us the location of the third point of our kite, let's call it $C$ .
This point is simultaneously $\text{4 cm}$ from $B$ and $\text{5 cm}$ from $B$ , which is exactly what we need!

Draw a line segment from the first intersection near $A$ (from step 2.1.2) to point $C$ .
Then, draw a line segment from the second intersection near $A$ (from step 2.2.2) to point $C$ .

You've now constructed the kite!
Don't erase those construction arcs – they show all the hard work you've done!

We've successfully drawn a kite with a diagonal of $\text{6 cm}$ and adjacent sides of $\text{4 cm}$ and $\text{5 cm}$ connected to one endpoint of the diagonal, using only a ruler and compass!