TrianglesTrianglesClassifications,

Angle Sum,Transformations

ClassificationsClassificationsTriangles can be classified with any combination of the three sides and the three angles.

Like:

Obtuse, Scalene

Acute, Equilateral

Which side classification can only be matched with one angle classification? why?

Sides

1) Scalene2) Isosceles

3) Equilateral

Angles

1) Acute2) Obtuse3) Right

Classification of Classification of triangles means triangles means

choosing the choosing the adjectives that adjectives that

describe the triangle.describe the triangle.When classifying triangles choose the adjectives that describe the angles and sides.

When there are more than one coordinate adjectives describing a noun they must be separated by a coma.

This problem shows one obtuse angle. Therefore it is an obtuse triangle.

There are two tick marks showing that two sides are congruent. Therefore, this triangle is also isosceles.

The two together is an obtuse, isosceles triangle.

There is a right angle, therefore it is a right triangle..

There are two tick marks showing two congruent sides, therefore it is an isosceles triangle too.

This triangle is a right, isosceles triangle.

The sides stand out with me the most so I immediately classify it as equilateral. All of the sides have tick marks, so this is an Equilateral triangle.

All of the angles are 600. (Why?) Therefore, it is an acute triangle.

This triangle is an Equilateral, acute triangle.

This triangle has one obtuse angle and two acute angles. That makes it an obtuse triangle.

There are no tick marks to show congruent sides. Since all of the angles are different the sides are also different. Therefore, this is a scalene triangle.

This is an obtuse, scalene triangle.

This triangle has all acute angles, therefore, it is an acute triangle.

There are no tick marks showing congruent sides and all of the angles are different, therefore, it is a scalene triangle.

This triangle is an acute, scalene triangle.

Interior angle sum for Interior angle sum for triangles.triangles.

The interior angle sum of the angles of a triangle is 1800.

Therefore when you need to find the missing angle add the angles that are there and subtract the sum form 180.

This problem can be done several ways.

First if you already remember that the angles of an equilateral triangle are 600, then you will know that the missing angle is 600.

However, you can also add 60 plus 60 to get 120 and subtract that form 180 to get ...60.

This problem can lead to algebra.

Since the sum of all of the angles you can write an algebraic equation that is set equal to 1800.

34+x+104+x = 180

Then solve this equation.

The final answer is 21.

This problem can also be done using algebra.

Add all of the angles. 5x=180.

Solve this problem to get 36.

Classification of Classification of triangles means triangles means

choosing the choosing the adjectives that adjectives that

describe the triangle.describe the triangle.When classifying triangles choose the adjectives that describe the angles and sides.

When there area more than one adjective describing a noun they must be separated by a coma.

The immediate side classification is equilateral.

Then the angles are all acute.

Therefore, this an acute, equilateral triangle.

This triangle gives very little clues.

It is necessary to add the two acute angles to find that the third missing angle is obtuse, 1400. Therefore, it is an obtuse triangle.

Since all of the angles are different so are the sides. Therefore this triangle is an obtuse, scalene triangle.

This picture clearly shows an obtuse angle.

It shows that two angles are congruent, therefore, the two sides opposite those angles are congruent.

This triangle is an obtuse, isosceles triangle.

This next portion asks This next portion asks us to draw the triangle us to draw the triangle

if possible.if possible.

I will attempt to draw these using the drawing tools available. Wish me luck.

This is a no-brainer, since we have already seen several.

Well it is harder to make than it is to see.

It was easier to select a triangle and insert it.

We also have seen this one.

I finally found the line segments!

This we haven’t seen! Be suspicious!

First think about it. Doesn’t an equilateral have all 600 angles? So how can one be greater than 900? It is impossible!

I believe we have seen at least on of these. You can check your review to see.

This looks like it is acute. However, it looks like one of the angles might be 900. This is possible but be aware of the 900 angle. Actually you can do this with arithmetic. Add different numbers less than 90 that add up to 180, like 80, 50, and 50.

Check to see if you have seen one of these on the review.

This one is sort of easy to draw. What do you notice about the congruent sides?

This problem goes back to the sun of the interior angles of a triangle is 1800.

This is on of the times where you can write an equation setting expressions equal to 180.

x+x-15+31 = 180

2x-16=180

2x = 24

x=12

x=

18) True: Since the definition of an isosceles triangle states that it must have at least two sides congruent.

19) False: There are many combinations of angle measures that add up to 180 where the acute angles are not congruent.

20) False: This question is tricky. There is a double negative here that means it is possible to draw an obtuse equilateral triangle. Since we just tried this we know it is impossible.

21) True: This question is also a double negative that means that it is possible to draw a right, isosceles triangle. We already drew one earlier so it can be done.

22) False: The Pythagorean theorem is for right triangles only.

TranslationsTranslations

Now you will need to identify if the triangles are translations, reflections, or rotations.

This picture has an arrow showing the type of transformation. There is also a point that the transformation is using. This is a rotation of 900 to the clockwise.

Here we see the arrow and point again. This is also a rotation of 3600 counterclockwise.

This one has two arrows and a dashed line between the pictures. The pictures also look lice reflection of each-other in a mirror. This is a reflection.

This picture has two arrows, straight arrows. The shape is not turned or reflected. It is a translation.

This picture also has two straight arrows. The arrows do not show any rotating or reflection lines. This is a translation.

Completing the Completing the Congruent StatementCongruent Statement

Completing the congruent statement requires determining the order of the letters given and repeating that order. The corresponding angles must be in the same order.

The triangle name they give is GHI. The G angle has one arc. The H has three arcs, and the I has two arcs. Therefore, the first letter of the missing name should start with one arc, followed by three arcs and then two arcs.

The name should be triangle PRQ.

This triangle name starts with B, three arcs, then C, one arc, then A, two arcs. Even though these two triangles share two points using the arcs will reduce the confusion.

The name should be D, three arcs, A, one arc, and C, two arcs, or triangle DAC.

H, one arc, K, two arcs, U, right angle

V, one arc, J, two arcs, T, right angle

VJT

Here the picture can be used to see the corresponding parts or the naming. Place the names on top of each other and the corresponding angles line up as well as the sides.

DEF

JKL

9) Since J is first and D is first they correspond.

10) Since EF is last and KL is last the segments are corresponding sides.

We can stack the We can stack the names to complete all names to complete all

of these.of these.STR

XYZ

11) The Z is last and the R is last.

12) The T is second and the Y is second.

13) XY are the first two letters and ST are the first two letters.

14) YZ are the last two letters and TR are the last two letters.

15) X is the first letter and S is the first letter.

We are back two the arcs. The name they give is SUT. S, one arc, U three arcs, and T two arcs

So the answer is T, one arc, S, two arcs, and R, three arcs or TSR.

D, one arc, E, right angle, F, two arcs

X, one arc, Y, right angle, Z, two arcs

XYZ

This transformation has a dashed line and a curved arrow. It is a reflection because of the line and the reflected sides.

This also has a reflecting line and curved arrows. It is a reflection.

DEF

XYZ

<D is congruent to <X

<E is congruent to <Y

< F is congruent to < Z

Line segment DE is congruent to line segment XY.

Line segment EF is congruent to line segment YZ.

Line segment DF is congruent to line segment XZ.

To mark the triangles place arcs according to the corresponding angles then place tick

marks for the corresponding sides.

CDE

PQR

<C is congruent to <P

<D is congruent to <Q

<E is congruent to <R

line segment CD is congruent to line segment PQ.

Line segment DE is congruent to line segment QR.

Line segment CE is congruent to line segment PR.

To mark the triangles place arcs according to the corresponding angles then place tick

marks for the corresponding sides.

After you finish your After you finish your review you should review you should

look over it.look over it.

Look over it once a day until you quiz or test.

Write down the problems that seem difficult.

Place stars next to them and review them after going over all os the review.