* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Name:
Survey
Document related concepts
Dessin d'enfant wikipedia , lookup
Line (geometry) wikipedia , lookup
Golden ratio wikipedia , lookup
Multilateration wikipedia , lookup
Technical drawing wikipedia , lookup
Apollonian network wikipedia , lookup
Euler angles wikipedia , lookup
History of geometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Transcript
Geometry Name: _________________________ Date: _______________ Per.: ______ 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 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 2 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) 3 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 4 Geometry VII. Proofs. Write a two-column proof. 1) 2) 3) MD/CR 1/14/Ch. 4 MT Review 5 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