two triangles are similar if and only if all three corresponding internal angles are congruent

SIMILAR TRIANGLES

Similar Triangles Formal Definition

Two Triangles are similar if and only if all three corresponding internal angles are congruent

Similar Triangles Formal Definition

Two Triangles are similar if and only if all three corresponding internal angles are congruent

Do we need to know all 6 anglesto prove triangles similar

Remember the sum of the interior angles of a triangles always equals 180 degrees

So if we know two angles we know the third

If 2 pairs of internal angles are congruent the third pair is also

AA Postulate

If 2 pairs of internal angles are congruent the third pair is also

Therefore if two triangles have two corresponding angles congruent the triangles are similar

AA Postulate

Definition Corresponding Sides

The side in each triangle opposite the congruent angle.

What?

Definition Corresponding SidesOne side in each triangle that is opposite the congruent

angle

The side in each triangle opposite the congruent angle

Similar TrianglesIf two triangles are similar then the ratios of the

corresponding sides are equal

90/45=2

100/50=2

80/40=2

If two triangles are similar then the ratios of the corresponding sides are equal We say the corresponding sides are proportional

Remember your work with ratiosa/x=b/y

Then we cross multiplyay=bxDividea/b=x/y

ThereforeIf two triangles are similar then the ratio between any two sides of one triangle is equal to the ratio between the corresponding sides in the other triangles. We say corresponding pairs are proportional

Similar Triangles

If two triangles are similar then the ratio between any two sides of one triangle is equal to the ratio between the corresponding sides in the

other triangles We say corresponding pairs are proportional

80/100=40/50

90/80=45/40

90/100=45/50

Pickup a set of instructionsGo to the computer

Click The Geometer's Toolkit ICON

Open the Similar Triangles ToolFollow the instructions on the

sheet you picked up

Similar Triangles and Transformations

Remember triangles remained congruent over reflection rotation and translation These transformations created congruent images.

Triangles also remain similar over reflection rotation transformation and can do under dilation. Dilation produces an image that is similar if the angles do not change.

Click Here To See

What Can we do with all this

We can use the information to find unknown parts of triangles

Tomorrow we will use what we learned to help us measure the height, length or width of various objects

What Can we do with all this

What Can we do with all this

What Can we do with all this

An Easy Way to Keep Track

YOU CAN TAKE YOU RATIOS EITHER HORIZONTALLY OR VERTICALLY

MAKE A CHART

SmallTriangle

LargeTriangle

Small Side

Medium Side

Large side orHypotenuse

4 8

y y+4

4/y=8/(y+4) or 4/8=y/(y+4)

Cross Multiply4(y+4)=8y

Divide by 4y+4=2y

Subtract y 4=y or y=4

SmallTriangle

LargeTriangle

Small Side

Medium Side

Large side orHypotenuse

4 8

y y+4

4/y=8/y+4 or 4/8=y/y+4

Cross Multiply4(y+4)=8y

Divide by 4y+4=2y

Subtract y 4=y or y=4

Links you may find helpful

http://www.mathopenref.com/similartriangles.htmlA great quick reference (you saw it earlier)http://www.glencoe.com/sec/math/brainpops/00112049/00112049.htmlA preview of tomorrow

http://library.thinkquest.org/20991/geo/spoly.html

“Math for Morons” always a good choice