Honors Geometry Name: ____________________________Date: ______________ Hour: _______

Chapter 4 Review1. Classify the triangles by their angles and sides.

a. △ABE b. △EDB

c. △EBC d. △DBC

2. Find y and the length of each side if △ABC is isosceles with AB = BC, AB=4y, BC=3y+2 and AC=2y.

3. Make sure you know and can use these theorems: a. Triangle Sum Theorem -

b. Exterior Angle Theorem –

c. Third Angle Theorem –

d. Postulates/Theorems that can be used to prove triangles are congruent:

e. Postulates/Theorems that can’t be used to prove triangles are congruent:

f. Isosceles Triangle Theorem –

g. Converse of Isosceles Triangle Theorem -

4. Find the measure of each angle in the picture.

5. Identify the type of congruence transformation shown as a reflection, translation, or rotation, and verify that it is a congruence transformation.

Honors Geometry Name: ____________________________Date: ______________ Hour: _______

6. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, write not possible.

a. b. c.

7. Write a two column proof. Given: ∠D ≅ ∠F, ¿ bisects ∠DEF.Prove: DG ≅ FG

Statements Reasons

8.

RC bisects∠ ACERC bisects∠ ACERC bisects∠ ACERC bisects∠ ACERC bisects∠ ACERC bisects∠ ACERC bisects∠ ACERC bisects∠ ACERC bisects∠ ACE

Honors Geometry Name: ____________________________Date: ______________ Hour: _______

9. Find x and the length of each side if △FGH is an equilateral triangle.

10. Position and label each triangle on the coordinate plane.Isosceles triangle △RST with base RS 4a units long

11. Write a coordinate proof for the statement. Prove that the segments joining the midpoints of the sides of a right triangle form a right triangle.

12. a. Given: m∠UZY = 90, m∠ZWX = 45, △YZU ≅ △VWX, UVXY is a square (all sides congruent, all angles right angles).

Find m∠WZY.

Honors Geometry Name: ____________________________Date: ______________ Hour: _______

b. Given: AC = AD, and AB ⊥ BD, m∠DAC = 44 and CE bisects ∠ACD.Find m∠DEC.

13. Study enrichments!

Honors Geometry Name: ____________________________Date: ______________ Hour: _______

Answers: 1.a. Right, Scalene

b. Obtuse, Isoscelesc. Right, Scalened. Equilateral, Equiangular

2. y=2, AB=8, BC=8 and AC=44. measure of angle 1 = 60, measure of angle 2 = 60 and measure of angle 3 = 1205. Rotation, AB = 2sqrt2, BC = 2sqrt2, CA = 4, DE =2sqrt2, EF = 2sqrt2, FD = 4. The triangles are congruent by SSS.6. a. Not Possible

b. SAS or SSS or HLc. SSS

7. ∠D ≅ ∠F, ¿ bisects ∠DEF. (Given) Segment GE is congruent to segment GE (Reflexive Prop.Angle DEG is congruent to angle GEF(Def. of Angle Bisector)Triangle DEG is congruent to triangle FEG (AAS)Segment DG is congruent to segment FG (CPCTC)8. Check flow proof with Ms. Gerst9. x = 9, FG = GH = FH = 3710.

11.

12. a. 45o

b. 78o