Download 4-1-angle-side-relationship-in-triangles-notes

Name___________________________________
4-1 Check In quiz
Geometry Period______
Date__________
You watched a video last night classifying triangles and determining angle measure given ratios.
Answer the following questions:
Triangle might not be drawn to scale
In triangle ABC, the angles are in the ratio 1:3:5, respectively. Solve for each angle. Fill into diagram
State the names of each angle, list them smallest to biggest
Classify the triangle in terms of its angles.
STOP AND WAIT!
State the medium length side of the triangle above. How did you get that?
Name___________________________________
4-1 Notes
Geometry Period______
Date__________
Today’s Learning Goal: What is the Side-Angle Relationship in triangles?
Angle-Side Relationships in Triangle
Consider ∆ABC as shown below with given side lengths and
angle measures:
Turn and Talk:
With your elbow partner, answer the three questions below
1) List the angles (by name) in order from smallest to biggest:
2) List the sides (by name) of the triangle in order from smallest to biggest:
3) Write a conjecture that describes a relationship between the measure of angles and the measure of sides:
BE PREPARED TO SHARE OUT!
Together!
Angle - Side Relationship
The ______________ side is across from the ______________ angle.
The ______________ side is across from the ______________ angle.
The ______________ side is across from the ______________ angle.
Let’s Try It!
Example 1) InΔ ABC, 𝑚∡A = 30° and 𝑚∡B = 50°. What is the name the longest side of the triangle?
Example 2)
Angle – Side Relationship Partner Playtime
Choose who will be partner peanut butter and who will be partner jelly. Work on your column’s questions. Each problem is different,
but your multiple choice answers should match. If there is a discrepancy between answers, figure out who is right and help your
partner correct their mistake. Work on the last 2 problems together
1
2
Partner Peanut Butter
In scalene triangle ABC,
and
.
What is the order of the sides in length, from
longest to shortest?
1)
2)
3)
4)
In
1)
2)
3)
4)
,
,
,
,
,
,
,
,
,m∠𝐶 < m∠𝐴 < m∠𝐵. Which inequality is
true?
In
1)
2)
3)
4)
In
1)
2)
3)
4)
,
sides of
are
,
,
,
,
Partner Jelly
and
= 70. The lengths of the
in order from smallest to largest
,
,
,
,
,
false?
. Which statement is
3
For which measures of the sides of
the largest angle of the triangle?
is angle B
1)
2)
3)
4)
For which measures of the sides of
smallest angle of the triangle?
1)
2)
3)
4)
AC = 12, AB = 10, BC =14
AC = 8, AB = 9, BC = 6
AC = 8, AB = 9, BC = 10
AC = 4, AB = 3, BC = 8
Peanut Butter Jelly Time! Try these as a team now
4) The degree measures of the angles of
are represented by x, 3x, and
.
Find the value of x. Classify this triangle by its angles.
5) As shown in the diagram of
If
,
below, B is a point on
, and
and
is drawn.
, what is the longest side of
?JUSTIFY your answer.
is angle B the
6) In
1)
2)
3)
4)
7)
,
,
, and B is a point on side
, such that
. Which line segment is shortest?
Name___________________________________
4-1 Homework
Geometry Period______
Date__________
1. In
,
, and
. Which expression correctly relates the lengths of the sides of this triangle?
1)
2)
3)
4)
2) Determine and state the largest angle of ∆𝑅𝑆𝑇, and justify how you obtained your answer.
3) In triangle RST, which is a possible side length for ST? (Select any that apply)
4) the accompanying diagram,
What does
is a straight line, and angle E in triangle BEC is a right angle.
equal?
1) 135°
3)
180°
2) 160°
4)
270°
5) In the diagram below of
with side
extended through D,
is the longest side? Justify your answer.
6) In
,
and
is an obtuse angle. Which statement is true?
1)
and
is the longest side.
2)
and
is the longest side.
3)
and
is the shortest side.
4)
and
is the shortest side.
and
. Which side of