Math Fourth Period 2.015

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Colegio Gimnasio Campestre San Sebastián

NOMBRE:_______________________________________________ GRADO: 8TH GRADE

PERIODO: FOURTH AREA: MATH MISS SOPHIE CORZO PÉREZ

Look at the images and answer some questions

a. What kind of figure are they?

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b. What kind of triangles are the figures?

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c. What are the main characteristics from the figures?

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d. Are the figures congruent? Argue your answer

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2. Describe a right triangle

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2. Draw images about the different kinds of triangles

Scalene

Isosceles Equilateral

3. What is a congruence, in geometry?

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4. Write the names of these numbers

a) 318,203,748: __________________________________________________________________

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b) 243, 734,302: _________________________________________________________________

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c) 945,912, 002: _________________________________________________________________

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d) 394,982, 920: _________________________________________________________________

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e) 242,894,918: __________________________________________________________________

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f) 391,683,802: __________________________________________________________________

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g) 784,084,731: __________________________________________________________________

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5. Write these number

a. Nine hundred and eighty-three million, seven hundred and twenty-one thousand and thirty-four:

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b. Nine hundred and eighteen million, two hundred and seventy-three thousand, six hundred and

forty-five: _________________________

c. Nine hundred and eighty-seven million, six hundred and fifty-four thousand, three hundred and

twenty-one: _____________________

d. Seven hundred and eighty-nine million, four hundred and fifty-six thousand, one hundred and

twenty-three: _____________________

e. Nine hundred and eighty-seven million, four hundred and fifty-six thousand, three hundred and

twenty-one: _____________________

f. Four hundred and thirty-two million, one hundred and fifty-six thousand, nine hundred and eighty-

seven: _____________________

6. Decrypt the message using the numbers and letters

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Key:

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Congruence of Triangles

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the

same shape and size as the mirror image of the other. More formally, two sets of points are

called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination

of rigid motions, namely translations, rotations and reflections. This means that either object can be

repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two

distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up

completely. Turning the paper over is permitted.

Congruence of two triangles

In elementary geometry the word congruent is often used as follows.

The word equal is often used in place of congruent for these objects.

Two line segments are congruent if they have the same length.

Two angles are congruent if they have the same measure.

Two circles are congruent if they have the same diameter.

In this sense, two plane figures are congruent implies that their corresponding characteristics are

"congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding

diagonals, perimeters and areas. The related concept of similarity applies if the objects differ in size but

not in shape.

What is "Congruent" ... ?

It means that one shape can become another using Turns, Flips and/or Slides:

Rotation

Turn!

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Reflection

Flip!

Translation

Slide!

Congruent Triangles

If two triangles are congruent they will have exactly the same three sides and exactly the same three

angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they

will be there.

Same Sides

If the sides are the same then the triangles are congruent. For example:

is congruent to:

and

because they all have exactly the same sides.

But:

is NOT congruent to:

because the two triangles do not have exactly the same sides.

Same Angles

Does this also work with angles? Not always! Two triangles with the same angles might be congruent:

is congruent to:

only because they are the same size

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But they might NOT be congruent because of different sizes:

is NOT congruent to:

because, even though all angles match, one is larger than the other. So just having the same angles is no

guarantee they are congruent.

Other Combinations

There are other combinations of sides and angles that can work ...

... read more at How To Find if Triangles are Congruent

Marking

If two triangles are congruent, we often mark corresponding sides and angles like this:

is congruent to:

The sides marked with one line are equal in length. Similarly for the sides marked with two lines and three

lines. The angles marked with one arc are equal in size. Similarly for the angles marked with two arcs and

three arcs. There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

1. SSS (side, side, side)

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.

For example:

is congruent to:

If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

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SAS (side, angle, side)

SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and

the included angle are equal. For example:

is congruent to:

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of

another triangle, the triangles are congruent.

3. ASA (angle, side, angle)

ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and

the included side are equal. For example:

is congruent to:

If two angles and the included side of one triangle are equal to the corresponding angles and side of

another triangle, the triangles are congruent.

4. AAS (angle, angle, side)

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AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and

the non-included side are equal. For example:

is congruent to:

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of

another triangle, the triangles are congruent.

5. HL (hypotenuse, leg)

This one applies only to right angled-triangles!

or

HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the

other two sides are called "legs") It means we have two right-angled triangles with the same length of

hypotenuse and the same length for one of the other two legs. It doesn't matter which leg since the

triangles could be rotated. For example:

is congruent to:

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and

leg of another right-angled triangle, the two triangles are congruent.

1. Answer these questions according to the text.

a. What is a congruence? _____________________________________________________________

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b. What does elements we need to take into account about the congruence? ______________________

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2. Draw two images showing the congruence in triangles and in polygons

Congruence in triangle

Congruence in polygons

3. Write the meaning of these words

a. congruence: __________________________________________________________________

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b. angle: _______________________________________________________________________

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c. triangle: _____________________________________________________________________

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d. polygon: _____________________________________________________________________

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4. Look for some words related with the kinds of graph in the word search

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1. Select the corresponding place for each couple of figures

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2. Write the names of these polygons taking into account the numbers of sides

4. Write the numbers of sides from each one of these items

Consult the biography about these recognized mathematicians

a. Newton

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b. Euler

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ASPECTS TO EVALUATE

YES

NO

I didn’t have any difficulty along the development of the worksheet.

I developed all the activities in order and dedication.

I felt myself comfortable doing all the activities.

I reinforced and acquired new knowledge to the activities planned in the

worksheet.