Download Do Now: Chapter 8: Right Triangles

Name:_______________________________________________
Date:____________________
Chapter 8: Right Triangles
Topic 5: Mean Proportions & Altitude Rules
Do Now: Use the diagram to complete all parts:
a) Find all three angles in each triangle.
b) Find side ZY
c) Are these triangles similar? Explain your answer.
Exploring a Proportion
- Remember the rule is that the product of the means equals the product
of the extremes.
- This proportion can be referred to as “Mean Proportional” or “Geometric Mean”
Examples:
1) Find the geometric mean of 4 and 18 in simplest
radical form.
3)
is the geometric mean of 6 and what number?
2) 25 is the geometric mean of 5 and what number?
Overlapping Triangles Notes
The altitude to the hypotenuse of a right triangle forms two
triangles that are similar to each other and to the original triangle.
Since these triangles are similar, we can establish proportions relating the
corresponding sides and solve for missing pieces of information.
Lets break apart the triangles:
Large Triangle
Left Triangle
The large and left triangles both contain:
1) a right angle <ACB and <ADC
2) <A (Reflexive Property)
Example:
1) Find the value of x.
Steps:
 Separate the triangles
Practice:
2) Find the value of x.
Can you identify a pattern??
ALTITUDE RULE:
Right Triangle
Now the left triangle is rotated clockwise.
The left and right both contain:
1) right angles <ADC and <CDB
2) <CAD rotated to <BCD
 Set up a proportion to solve
Practice:
5) Find the value of x.
6) Find the value of x.
7) Find the value of x.
8) Find the value of x
Name:_______________________________________________
Date:____________________
Mean Proportions and Overlapping Triangles Homework
1) Find the geometric mean of 3 and 48.
2) Find the geometric mean of 4 and 10 in
simplest radical form.
3)
4) Find the value of x.
is the geometric mean of 12 and
what number?
5) Find the value of x.
7) Find the value of x.
6) Find the value of x.
Review Section:
_____ 8.) In
m<A = 95 and m<B = 50 and m<C = 35. Which expression correctly relates the
lengths of the sides of this triangle?
(1)
(2)
(3)
(4)
_____ 9.) Point P is on line m. What is the total number of planes that are perpendicular to line m and
pass through point P.
(1) 1
(2) 2
(3)0
(4) infinite
_____ 10.) 7, 9, and 10 can be the lengths of the sides of a triangle.
(1) true
(2) false
11.) In the diagram below of trapezoid RSUT, RS||TU, X is the midpoint of RT, and
V is the midpoint of SU. If RS=3x + 7 , XV=3x + 17, and TU = 5x + 11, find the
value of x and the length of all three segments.
12.) The vertex of an isosceles triangle is four times the measure of a base angle. Find the measure of all three
angles of the isosceles triangle.
13.) In two complementary angles, the measure of one angle is 6 more than twice the measure of the other.
Find the measure of both angles.
Name:_______________________________________________
Date:____________________
Chapter 8: Right Triangles
Topic 5: Mean Proportions & Right Triangle Rules DAY 2
Do Now: Find the value of x.
1) Find the value of x.
2) Find the value of x.
3) Find the value of x.
4) Find the value of x.
5) Find the value of x.
6) Find the value of x and y in simplest radical form.
7) Find the value of x, y and z to the nearest tenth.
8) Find the value of x.
9) Find the value of x, y and z to the nearest hundredth.
Name:_______________________________________________
Altitude & Leg Rule Day 2 Homework
1) Find the value of x.
2) Find the value of x.
3) Find the value of x.
4) Find the value of x, y and z to the nearest tenth.
Date:____________________
5) Find the value of x.
Review Section:
6) Express
_____7) In
(1) XV
(3) VW
in simplest radical form.
and PM is the shortest side of
(2) WX
(4) NP
_____8) As shown in the diagram below, CD is the median of
Which statement is always true?
(1)
(2)
(3)
(4)
, what is the shortest side of
.
_____ 9) Plane A and Plane B are two distinct planes that are both perpendicular to line l. Which statement
about planes A and B is true?
(1) Planes A and B have a common edge, which forms a line
(2) Planes A and B are peperndicular to each other
(3) Planes A and B intersect each other at exactly one point
(4) Planes A and B are parallel to each other
10)
ABC is similar to DEF. The lengths of the sides of
side of
if its perimeter is 60?
are 5, 8, and 11. What is the length of the shortest
11) The equation of a line is
. What is an equation of the line that is perpendicular to the given
line and that passes through the point (4,2)?