Geometry Semester 1 Final Review PDF

# Geometry Semester 1 Final Review ## Unit 1: Transformations and Symmetry 1. Describe the transformations for the following * **a.** Translate $(x, y) \to (x - 5, y + 3)$ * **b.** Rotate $90^\circ$ clockwise about point $F$. Then translate $(x, y) \to (x - 3, y - 3)$. * **c.** Reflec...

# Geometry Semester 1 Final Review ## Unit 1: Transformations and Symmetry 1. Describe the transformations for the following * **a.** Translate $(x, y) \to (x - 5, y + 3)$ * **b.** Rotate $90^\circ$ clockwise about point $F$. Then translate $(x, y) \to (x - 3, y - 3)$. * **c.** Reflect over $y = x$. * **d.** Rotate $90^\circ$ counterclockwise about point $M$. Then translate $(x, y) \to (x - 2, y - 2)$. 2. Translate using the following rule $(x, y) \to (x - 3, y - 5)$. Translate $\triangle DEF$, $(x, y) \to (x - 3, y - 5)$. 3. Rotate $XYZ$ $90^\circ$ counterclockwise about point $D$. ## Unit 2: Constructions, Congruence and Proof 1. Construct the following * **a.** Rhombus that contains side $AB$ and $\angle B$ * Circle $B$ with $\overline{AB}$ as radius * Circle $C$ * Circle $A$ * **b.** Perpendicular Bisector to $\overline{DE}$. 2. State if the following triangles are congruent. If congruent, give the theorem and finish the statement. * **a.** $\triangle GHI \cong \triangle ARE$, by $ASA$. * **b.** $\triangle DEF \cong \triangle ZYX$ by $SAS$. * **c.** $\triangle ABC \cong \triangle ILH$ by $SSS$. * **d.** $\triangle ABC \cong \triangle YDE$ by $ASA$. 3. Describe a series of transformations to prove that the following triangles are congruent. * **1.** Translate $\triangle ABC$ until point $A$ coincides with point $I$. * **2.** Rotate $\triangle ABC$ until it coincides with $\triangle IHG$. ## Unit 3: Geometric Figures 1. Identify the angle type (name): * **a.** Corresponding * **b.** Same-Side Interior * **c.** Alternate Interior * **d.** Vertical * **e.** No relationship 2. Identify the angle relationship (congruent or supplementary): * **a.** Congruent * **b.** Supplementary * **c.** Congruent * **d.** Congruent * **e.** Supplementary 3. Prove the following * **Given:** $\overline{AB} \parallel \overline{CE}$ * **Prove:** $\angle DAB + \angle ABD + \angle ADB = 180^\circ$ | Statement | Reason | |---|---| | 1) $\overline{AB} \parallel \overline{CE}$ | 1) Given | | 2) $\angle 1 \cong \angle 4$ | 2) Alternate Interior | | 3) $\angle 2 \cong \angle 5$ | 3) Alternate Interior | | 4) $\angle 4 + \angle 3 + \angle 5 = 180^\circ$ | 4) Linear Pair | | 5) $\angle 1 + \angle 2 + \angle 3 = 180^\circ$ | 5) Substitution | 4. Prove the following * **Given:** $\overline{AB} = \overline{CB}$ * **Given:** $\overline{BD}$ bisects $\angle ABC$ * **Prove:** $\angle DAB = \angle DCB$ | Statement | Reason | |---|---| | 1) $\overline{AB} = \overline{CB}$ | 1) Given | | 2) $\overline{BD}$ bisects $\angle ABC$ | 2) Given | | 3) $\angle ABD = \angle CBD$ | 3) Definition of bisector | | 4) $\overline{BD} = \overline{BD}$ | 4) Reflexive | | 5) $\triangle ABD \cong \triangle CBD$ | 5) SAS | | 6) $\angle DAB \cong \angle DCB$ | 6) CPCTC | ## Unit 9: Probability 3. Out of 493 cars, complete the two-way table below. And then answer the questions. | Type of Car | Ford | Toyota | Total | |---|---|---|---| | New | 133 | 179 | 312 | | Used | 101 | 80 | 181 | | Total | 234 | 259 | 493| * **a**. What is the probability of randomly selecting a new Toyota car? $\frac{179}{493} \approx 0.363 \approx 36.3%$ * **b**. What is the probability of randomly selecting a Ford car? $\frac{234}{493} \approx 0.474 \approx 47.4%$ * **c**. What is the probability of randomly selecting a used car given it is a Toyota? $\frac{80}{259} \approx 0.308 \approx 30.8%$ ## Unit 4: Quadrilaterals 5. Prove the following * **Given:** $ABCD$ is a parallelogram * **Prove:** $\overline{AB} = \overline{CD}$ | Statement | Reason | |---|---| | 1) $ABCD$ is a parallelogram | 1) Given | | 2) $\overline{AB} \parallel \overline{CD}$ | 2) Definition of parallelogram | | 3) $\overline{BC} \parallel \overline{AD}$ | 3) Definition of parallelogram | | 4) $\overline{CB} = \overline{CB}$ | 4) Reflexive | | 5) $\angle ABC \cong \angle DCB$ | 5) Alternate Interior | | 6) $\angle CAB \cong \angle CDB$ | 6) Alternate Interior | | 7) $\triangle ABC \cong \triangle CDB$ | 7) ASA | | 8) $\overline{AB} = \overline{CD}$ | 8) CPCTC | 6. Prove the following * **Given:** $\overline{BF} \parallel \overline{AD}$ * **Prove:** $\angle 3$ and $\angle 7$ are congruent corresponding angles | Statement | Reason | |---|---| | 1) $\overline{BF} \parallel \overline{AD}$ | 1) Given | | 2) $\angle 5 + \angle 7 = 180^\circ$ | 2) Linear Pair | | 3) $\angle 3 + \angle 5 = 180^\circ$ | 3) Same-Side Interior | | 4) $\angle 3 + \angle 5 = \angle 5 + \angle 7$ | 4) Transitive | | 5) $\angle 3 = \angle 7$ | 5) Subtraction |