Download MIDTERM E×Ah~: Chapter 4 Review

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MIDTERM E×Ah~: Chapter 4 Review - Congruent Triangles
Key Concepts & Skills
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)
Key Points
Triangles can be classified by their sides and by their angles.
Triangle Sum Theorem
MD/1-08/Ch. 4 MT Review
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Geometry
When two figures are congruent their corresponding sides and
corresponding angles are congruent. In the diagram AABC ~ AXYZ.
Z
Triangle Congruence Theorems and Postulates
~1’ ¢Oll~’tlcllt to OllC ~llothcr. Bdow ar~ the ~ombinations that WEbL work,
SSS
SAS
If ~.vo sides and the hMudcd angle of one trian~¢ arc con~x~nt to
th~ con’¢spondh~g pa~s of another ~4angle, the ~%a~¢~ arc
ASA
If hvo angles and the iucludcd side of one hlan~¢ are con~ent to
the con-cspon(~g parts of another ~4angl¢ tl~ Man~es alle
If V, vo angles and the non-inch,dzd side of
z~S ¢on~,~nt to the con’¢spondb~g pa~s of anoth¢~
If the hypotcmlse and leg of one r~ght tl"~m~e are eongn~ent to the
conespondh~ p,qlqs of anolher right triangle, the right tfian~es are
¢on~alent.
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.
Problems
I. Classify the triangle by sides and angles.
One acute angle of a right trim~gle measures 37°. Find the measure of the
other acute angle.
6,, In ~ MNP, the lneasttre of ~M is 24°, The measure of Z_N is five titr~s the
meas~re of ~ P. Find mz.N and m~/ E
MD/1-08/Ch. 4 MT Review
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Geometry
II. Congruence and Triangles. Use the figure to the right of ~ABC and ~XYZ
1.
Identify tl~e congruent co~’respo~ding parts ol’ti~e wiang!.es.
2. G yen ~’t_..*~, = 48° and n~Z = 37°. find ~lg~ Y.
III, Proving Triangles are Congruent.
I) Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell which
postulate or theorem you woutd use.
~_
,T
~
F
E
IV. Isosceles, Equilateral, and Right Triangles. Find the value of x.
4)
3)
2x+
MD/1-OS/Ch. 4 MT Review
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V. Proofs. Write a two-column proof.
PROVE ~A~’ ~ A~
A
2)
3)
A
MD/1-08/Ch~ 4 MTReview
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