Download TRI 01 Worksheet HW 28 Name_____________ Geometry 2013

TRI 01 Worksheet HW 28
Geometry 2013
Name_____________
Triangles can be classified by both their ANGLES and by the relative lengths of their SIDES.
Complete the table with classification criteria:
Classifications (by angles)
Acute
Obtuse
If the Largest Angle
between ____ º & ___ º
is______, then the triangle less than ___ º
…acute.
…obtuse
is…
Example:
97º
27º
80º
73º
Right
exactly =___ º
…right
50º
10º
73º
90º
40º
Now classify the following triangles in terms of angles only.
1) In Geometry, we are NEVER allowed to guess at an angle’s measure (we don’t assume without
evidence). However, pretend that rule doesn’t apply for just a moment. Based upon the picture,
classify the triangles below:
________________
_____________
_________________
_____________
2) Now, use good Geometry skills to deduce the angle classification of each triangle below.
(Remember, the sum of the interior angles in any triangle add up to 180º.)
105º
20º
??º
90º
70º
______________
??º
60º
10º
60º
80º
60º
100º
_______________ ________________ ______________ ________________
Equilateral
Isosceles
all three
at least 2
…equilateral …isosceles
Classifications (by sides)
A triangle with _______ congruent
sides is called….
Scalene
NO
…scalene
Now classify the following triangles in terms of sides only.
3) In Geometry, we are NEVER allowed to guess at a side’s length (we don’t assume without
evidence). However, pretend that rule doesn’t apply. Based upon the picture, classify the triangles
below:
________________
_____________
_________________
_____________
4) Now, use good Geometry skills to deduce the side length classification of each triangle below.
3
4
2
5
______________
4
8
8
8
6
8
6
??
______________* ________________ ______________ ________________
* notice anything?
5) Now classify the following triangles by BOTH angles AND side length (say Angle then Side)
3
53º
90º
80º
4
37º
5
_______ ______
50º
??º
??º
50º
_______ _______
60º
60º
_______ _______
10º
??º
60º
_______ _______
10º
??º
_______*_______
Geometry HW 28
Name: __________________
TRI Unit
Period: _____ Date________
TRI01: Define and classify triangles by sides and angles.
Classify each triangle below by both sides and angles.
5cm
80
30
70
3cm
90
8 ft
4cm
60
60
45
45
100
18 ft
By angle =>
By side =>
Sketch a triangle, including appropriate marks or labels to match the following classifications:
1) acute, isosceles
2) obtuse scalene
TRI02: Fill in the missing steps for the following proof of the Triangle Angle Sum Theorem.
8 ft
Unit 5: TRI - Triangles: Attributes, Congruence and Proof
SKILL
DESCRIPTION
TRI 01
Define and classify triangles by sides and angles.
TRI 02
Fill in the missing statements/reasons in a 2 column proof of the Triangle Angle Sum Theorem.
TRI 03
Given two angles of a triangle, find the third. Given algebraic expressions for the three angles in a
triangle, solve for x and find the measure of each angle.
TRI 04
State the corollaries to the Triangle Angle Sum Theorem
a) In a triangle, no more than one angle can be greater than or equal to 90 degrees. (this is a
proof by contradiction).
b)
In a right triangle, the two non-right angles are complementary.
c) If two angles of one triangle are congruent to two angles of another, then the third angles
are also congruent.
TRI 05
State and apply the Remote Interior Angles Theorem (aka Exterior Angle Theorem). Solve
problems, given exterior and remote interior angles, using algebra.
TRI 06
Define polygon congruence.
TRI 07
Given two polygons, determine if they are congruent by the Definition of Polygon Congruence.
TRI 08
Given two congruent polygons (especially triangles), write polygon congruence statement and
identify congruent corresponding parts.
TRI 09
Use SSS, SAS, ASA, AAS to determine if 2 triangles are congruent.
TRI 10
Be able to distinguish ASS from RHL, and use RHL to determine if two triangles are congruent.
TRI 11
Write two column proofs to establish simple triangle congruence.
TRI 12
Write simple triangle congruence proofs in a Flow Proof format.
TRI 13
Write two column or flow proofs for more complicated triangle congruence (including Reflexive,
Symmetric, Parallel Lines, Vertical Angles, CPCTC, etc.).
TRI 14
Apply the concepts of Isosceles Triangle Theorem and its Converse in solving algebraic equations.
TRI 15
Prove Isosceles Triangle Theorem in each of four ways: Given an isosceles triangle and ONE of
the following: altitude, angle bisector or median, prove that base angles are congruent.
TRI 16
Prove the Converse of the Isosceles Triangle Theorem.
TRI 17
Use Triangle Inequality Theorem to determine if three given sides form a triangle. Also be able to
determine the range of values for a third side, given the other two.
TRI 18
Given two angles in a scalene triangle, list the triangle’s side lengths in descending order and vice
versa.
TRI 50
Given a triangle and designated parts, construct significant segments.
TRI 99
a)
Given a triangle and a designated vertex, construct the median.
b)
Given a triangle and a designated vertex, construct the altitude.
c)
Given a triangle and a designated vertex, construct the angle bisector.
d)
Given a triangle & a designated side, construct perpendicular bisector.
Solve problems you haven’t seen before, using analysis and synthesis of the information learned so
far.