Name: _______________________________________________________
Day 26: Special Relationships within Right triangles SAAS
Opening Exercise: In DABC pictured below,
see?
Date:________________
Geometry CC (M2L21)
ÐB is a right angle and BD is the altitude. How many triangles do you
Below is a sketch of the triangles separated so that we can see them more clearly.
a. Is the large triangle similar to the
small triangle? Explain.
b. Is the large triangle similar to the
medium triangle? Explain.
c. What is the relationship between
the small triangle and the medium
triangle? How do you know?
Special Relations within Right Triangles
The altitude drawn from the right angle of a RIGHT LARGE triangle divides that triangle into two smaller triangles (one
small, one medium) which are BOTH similar to the original triangle.
---------------------------------------------------------------------------------------------------------------------------------------------------------------Example 1: Identifying pieces of the triangles
In each of the following examples where an altitude has been drawn from the right angle of a right triangle label the
pieces we have discussed above: Hypotenuse,Leg1, Leg2, Altitude, Segment1 and Segment2
a)
c)
b)
Example 2: KING OF THE MOUNTAIN when you do have the altitude (using segments)
(ALWAYS MAKE SURE YOUR PAPER HAS THE MOUNTAIN TOP ON TOP---The right angle in the big triangle)
Use similar triangles to find the length of the altitudes labeled with variables in each triangle below.
a.
b.
c.
Practice:
1. Solve for x:
2. Solve for z:
**When you Do have the altitude in the diagrams, what goes on the diagonals in the proportion?
SAAS HOMEWORK!
1.In the diagram to the right an altitude is formed from the
right angle in a right triangle. Using the variables in the
diagram, set up the proportion. (just letters)
2. Solve for x:
3. Solve for x:
Name: _______________________________________________________
Day 26 Continued: HLLS
Date:________________
Geometry CC (M2L21)
a) Label the pieces we have discussed as: Hypotenuse,Leg1, Leg2, Altitude, Segment1 and Segment2
Exploration: What is the difference in the missing pieces in Picture A or Picture B?
Picture A
Picture B
**KING OF THE MOUNTAIN when you don’t have the altitude****(using hypotenuse and legs)
Example 1: Find x
Example 2: Find x
“
h
e
le
g
is
th
e
***When you don’t have the altitudes in the diagram, what goes on the diagonals in the proportion?m
e
a
n
pr
o
p
**Example 3: Find x
Practice:
1. Find x
2.
Mixed Practice HLLS and SAAS
1. In the diagram below of right triangle ACB, altitude
If
and
, what is the length of
is drawn to hypotenuse
.
?
2. Four streets in a town are illustrated in the accompanying diagram. If the distance on Poplar Street from M to P is 9
miles and the distance on Maple Street from E to M is 10 miles, find the distance on Maple Street, in miles, from F to P.
3.In the diagram below of right triangle ACB, altitude
in simplest radical form.
intersects
at D. If
and
, find the length of
4. Find x
5. Find x
6. Find x
HLLS Homework
1. Solve for x
2. Solve for x:
3. Solve for x:
4.
x
z
y
4
9
5. Find the missing values. (If not a whole number, round to the nearest hundredth)
x
12
5
y
z
7. A geometry student says; “I got lost in that lesson - I wrote down that AB2  AD  AC but I have no idea where it
comes from.” Help this student - explain where AB2  AD  AC comes from.
B
o
A
x
D
Name: _______________________________________________________
Day 26: Special Relationships within Right Triangles Summary Slip
Date:______________
Geometry CC (M2L21)
1. A geometry student says; “I got lost in that lesson - I wrote down that z 2  x y for the diagram below, but I have no
idea where it comes from.” Help this student - explain where z 2  x y comes from.
C
Turn Over 
Name: _______________________________________________________
Day 26: Special Relationships within Right Triangles Summary Slip
Date:______________
Geometry CC (M2L21)
1. A geometry student says; “I got lost in that lesson - I wrote down that z 2  x y for the diagram below, but I have no
idea where it comes from.” Help this student - explain where z 2  x y comes from.
Turn Over 
2. A geometry student says; “I got lost in that lesson - I wrote down that p 2  k m for the diagram below, but I have no
idea where it comes from.” Help this student - explain where p 2  k m comes from.
2. A geometry student says; “I got lost in that lesson - I wrote down that p 2  k m for the diagram below, but I have no
idea where it comes from.” Help this student - explain where p 2  k m comes from.
INDEX CARD to demonstrate similar triangles.
This matches the example from the warm up!