Homework 5A.1: Parallel Lines and TransversalsDirections: Name each of the following types of angles. Then, state whether they are congruent or supplementary.

Name: Name:

Congruent or

Supplementary

Congruent or

SupplementaryName: Name:

Congruent or

Supplementary

Congruent or

Supplementary

Directions: Find the value of x in each question given that lines l and m are parallel. Check your answers by finding the measure of each angle.

5.

6.

7.

x =

m<C =

m<F =

x =

m<D =

m<F =

x =

m<B =

m<G =

Directions: Solve for the following. Show all work in the space provided.

9. In the accompanying diagram, line ℓ is parallel to line m, and line t is a transversal. Which must be a true statement?

(1) (3)

(2) (4)

10. The accompanying diagram shows two parallel roads, Hope Street and Grand Street, crossed by a transversal road, Broadway. If what is the measure of (1) 40° (3) 110°

(2) 70° (4) 180°

11. In the accompanying figure, what is one pair of alternate interior angles?

(1) 1 and 2 (3) 4 and 6

(2) 4 and 5 (4) 6 and 8

12. Find the value of x and y.

Homework 5A.2: Triangle Proofs

8.

x =

m<4 =

m<10 =

Math 3

1. Given: RS≅ RU ,TS≅ TU , ¿ S≅<U ,<SRT ≅<URT Prove: ∆ RST ≅ ∆ RUT

2. Given: RS≅UT ,RT ≅ SU Prove: ∆ RST ≅ ∆UTS

3. Given: AB≅ AD ,<B≅<D ,¿ ACB∧¿ACD are90°

Prove: ∆ ABC ≅∆ ADC

4. Given: LM ≅ PO ,<L≅<P ,<M∧¿Oare90 ° Prove: ∆ LMN ≅ ∆ PON

5. Given: H isthemidpoint of GJ ,GI ≅ IJ Prove: ∆GHI ≅∆ JHI

6. Given: M is themidpoint of >, M is themidpoint of HS

Prove: ∆GMH ≅∆TMS

7. Given: ¿ B∧¿Dare90 ° , AEbisects BD Prove: ∆ ABC ≅∆ EDC

8. Given: DC∨AE , DE≅ AC , Bis themidpoint of AE Prove: ∆ BDE≅ ∆BCA

Homework 5A.3 – Proving Parallelograms Practice

12)

Homework 5A.4 – Quadrilaterals

Directions: For questions #1-2, find the measure of each missing angle.1. 2.

Directions: For questions #3-4, find x and the length of EF.3. 4.

Directions: For questions #5-6, find the measures of the numbered angles in each kite.

5. 6.

Challenge Question: Solve for the unknown angle measures in the kite shown below.

Homework 5A.5 – Parallelogram & Quadrilaterals Review

1. Use the diagram below to solve for x and y if the figure is a parallelogram.

a) PT = 2x, QT = y + 12, TR = x + 2, TS = 7y

b) PT = y, TR = 4y -15, QT = x + 6, TS = 4x - 6

2. Find the measure of each angle if the figure is a rhombus.

a) Find the m∠1. b) Find the m∠2.

c) Find the m∠3. d) Find the m∠4.

3. Solve for x if the figure is a rhombus. 4. Solve for x if the figure is a rectangle.

5. What is the length of LN if the figure is a rectangle?

6. Solve for the missing angle measures if the figure is a rhombus.

7. What is the length of SW? 8. Solve for x in the figure if it is a rhombus.

Unit 5A – Logic and Reasoning Review