* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download MIDTERM E×Ah~: Chapter 4 Review
Survey
Document related concepts
Dessin d'enfant wikipedia , lookup
Penrose tiling wikipedia , lookup
Multilateration wikipedia , lookup
Noether's theorem wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Four color theorem wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Technical drawing wikipedia , lookup
Apollonian network wikipedia , lookup
History of geometry wikipedia , lookup
Euler angles wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Transcript
Name: Date: Per.: 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 1 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 2 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 3 V. Proofs. Write a two-column proof. PROVE ~A~’ ~ A~ A 2) 3) A MD/1-08/Ch~ 4 MTReview 4