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