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Geometry
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MIDTERM EXAM: Chapter 4 Review – Congruent Triangles
Vocabulary:
Equilateral Triangle
Obtuse Triangle
Isosceles Triangle
Vertex of a Triangle
Scalene Triangle
Adjacent sides of a
triangle
Legs of a right triangle
Equiangular Triangle
Acute Triangle
Vertex Angle
Pythagorean Theorem
Legs of an Isosceles
Triangle
Base of an Isosceles
Triangle
Interior angle
Congruent
Exterior Angle
Right Triangle
Base Angle
Hypotenuse
Corresponding Angles
Corresponding Sides
Textbook Sections: 4.1 – 4.6, 4.8, 5.3, 5.5, 8-2
Key Concepts & Skills
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Classify triangles by angles and sides (4.1)
Apply the triangle sum theorem and the exterior angle theorem to find the measures of angles of
triangles (4.1)
Identify congruent corresponding parts of triangles and write congruence statements (4.2)
Use triangle congruence to find measures of angles or sides (4.2)
Prove triangles are congruent using congruence postulates or theorems: SSS, SAS, ASA, and
AAS (4.3 and 4.4)
Decide whether it is possible to prove triangles are congruent and, if so, tell which postulate or theorem
applies (4.3 and 4.4)
Use congruent triangles to write proofs (4.5)
CPCTC—Corresponding Parts of Congruent Triangles are Congruent (4.5)
Plan for a proof (4.5)
Write two-column or paragraph proofs (4.3—4.5)
Pythagorean Theorem and its Converse
Triangle Inequality Theorem
Recognize and apply properties of inequalities to the measures of the angles/sides of a triangle.
Key Points
When two figures are congruent their corresponding sides and
corresponding angles are congruent. In the diagram ABC  XYZ.
Triangle Congruence Theorems and Postulates: SSS, SAS, ASA, AAS, HL
CPCTC – Corresponding Parts of Congruent Triangles are Congruent
Only used to prove corresponding parts of two triangles are congruent IF the two triangles are known to be
congruent or AFTER the two triangles are proven to be congruent.
MD/CR 1/14/Ch. 4 MT Review
1
Geometry
Problems
I. Triangles and Angles
Classify triangles by sides and angles.
5)
One acute angle of a right triangle measures 37o. Find the measure of the other acute angle.
6)
In DMNP , the measure of angle M is 24o. The measure of angle N is five times the measure of
angle P. Find the measures of angles N and P.
7)
Two angles are supplementary. One angle has a measure that is five less than four times the other.
What is the measure of the larger angle.
8)
Find the measures of angles 1 and 2.
9)
Find the measures of the missing angles.
10)
Find the value of x.
11)
Find the value of x.
MD/CR 1/14/Ch. 4 MT Review
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Geometry
II. Congruence and Triangles. Use the figure to the right of ABC and XYZ
1.
2.
III. Proving Triangles are Congruent.
1) Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell which
postulate or theorem you would use.
a)
b)
c)
IV. Isosceles, Equilateral, and Right Triangles. Find the value of the variable and the measure of the
corresponding side or angle. (Problems from the textbook)
1)
2)
3)
4)
MD/CR 1/14/Ch. 4 MT Review
5)
6)
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Geometry
7)
Find the measures indicated.
mÐCAD
mÐACD
mÐACB
mÐABC
mÐBAC
V. Triangle Inequalities
1) Write the side and angle measurements in order from least to greatest.
a)
2)
b)
Use the figure to the right to determine the relationship
between the lengths of the given sides.
a) DH, GH
b) DE, DG
c) EG, FG
d) DE, EG
VI.
Decide whether the numbers can represent the side lengths of a triangle. If they can,
classify the triangle as acute, right, or obtuse.
1)
6, 7, 10
2)
9, 40, 41
3)
8, 12, 20
4)
3, 4 5 , 9
MD/CR 1/14/Ch. 4 MT Review
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Geometry
VII. Proofs. Write a two-column proof.
1)
2)
3)
MD/CR 1/14/Ch. 4 MT Review
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Geometry
4)
Given:
MP @ KJ
and
ÐK @ ÐM
Prove: L is the midpoint of
5)
Given:
XQ ||TR
Prove:
QT bisects XR
and
MD/CR 1/14/Ch. 4 MT Review
XR
KM .
bisects
QT
6