10.1 Similar Right Triangles Learning Objective: To recognize relationships among the triangles...
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10.1 Similar Right Triangles Learning Objective: To recognize relationships among the triangles formed by the altitude to the hypotenuse of right triangle, to find the geometric mean of two numbers and to use similar triangles to estimate lengths. Warm-up (IN)
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Transcript of 10.1 Similar Right Triangles Learning Objective: To recognize relationships among the triangles...
10.1 Similar Right TrianglesLearning Objective: To recognize relationships among the triangles formed
by the altitude to the hypotenuse of right triangle, to find the geometric mean of two numbers and to use similar triangles to estimate lengths.
Warm-up (IN)
Notes
Learning Objective: To recognize relationships among the triangles formed by the altitude to the hypotenuse of right triangle, to find the geometric mean of two numbers
and to use similar triangles to estimate lengths.
Similar right triangle theorem -
If the altitude is drawn to the hypotenuse of a right triangle, then the 2 triangles formed are similar to the original triangle and to each other.
A
BC
D ~ABC ACD ~ CBD
Learning Objective: To recognize relationships among the triangles formed by the altitude to the hypotenuse of right triangle, to find the geometric mean of two numbers
and to use similar triangles to estimate lengths.
Geometric Mean -
b
x
x
aIf a, b, and x are positive numbers, and
Then, x is the geometric mean of the 2 numbers.
EX 1 – Find the geometric mean of 3 and 15.
15
3 x
x
2x 45x 53
Learning Objective: To recognize relationships among the triangles formed by the altitude to the hypotenuse of right triangle, to find the geometric mean of two numbers
and to use similar triangles to estimate lengths.
AB
C
D
BD
C
A
DC B
A
C
Learning Objective: To recognize relationships among the triangles formed by the altitude to the hypotenuse of right triangle, to find the geometric mean of two numbers
and to use similar triangles to estimate lengths.
Geometric Mean Theorems -
* If the altitude is drawn to the hypotenuse of a right triangle, then the length of the altitude is the geometric mean of the lengths of the segments of the hypotenuse.
A
BC
D
x
a
b
Learning Objective: To recognize relationships among the triangles formed by the altitude to the hypotenuse of right triangle, to find the geometric mean of two numbers
and to use similar triangles to estimate lengths.
* If the altitude is drawn to the hypotenuse of a right triangle, then the length of the each leg is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that leg.
A
BC
Dx
a bA
BC
D
x
a
b
EX 2 – Find the missing variables.
Learning Objective: To recognize relationships among the triangles formed by the altitude to the hypotenuse of right triangle, to find the geometric mean of two numbers
and to use similar triangles to estimate lengths.
9w
u
v
15
9
9u
15u15 81u 4.5v 6.9
w
w4.5
6.92w 84.51 w 2.7
4.515
EX 3 – Aida wants to buy a ladder that reaches the roof of her home. To do this, she holds a notebook near her eye and backs away form the house until the edge of the roof and the base of the house are in line with the notebook’s edges. She then measures he distance from the house. Use this information to
find the height of the roof.
5.7
5.7
5
5h 5 5h 25.56
h5 25 25.56h5 25.81h feet25.16
HW – tbd
Out – Describe some things that are true when you draw an altitude of a right triangle.
Summary – Wow. I can probably use then when…
