# Geometry 27 January 2014 - PowerPoint PPT Presentation

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Geometry 27 January 2014. WARM UP 1) Complete Using Congruent Triangles handout 2) Place Khan video notes on top of group folder FINISHED? Work on Geometry Proof Practice Review- Triangle Congruency Shortcuts SSS, SAS but not SSA SAA (AAS), ASA but not AAA

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Geometry 27 January 2014

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### Geometry 27 January 2014

WARM UP

1) Complete Using Congruent Triangles handout

2) Place Khan video notes on top of group folder

FINISHED? Work on Geometry Proof Practice

Review- Triangle Congruency Shortcuts

SSS, SAS but not SSA

SAA (AAS), ASA but not AAA

CPCTC- corresponding parts of congruent

triangles are congruent!

### Objective

Students will be able to prove and apply polygon properties.

HOMEWORK- DUE FRIDAY

pg. 283: 1 – 6; pg. 304: 7 – 12; pg. 300: 1, 3, 4

Properties of Parallelograms Handout

UNIT 5 TEST- FRIDAY We will NOT have time to go over homework questions before the test.

ANSWERS will be posted Wed/Th– see me w/ ?’s

### Complete Properties of QUADRILATERALS Handout

Think- Fill in as many properties of sides/ angles/ diagonals as you can

PAIR- TRADE- trade with a partner– do you see more they need to add? Use a different color.

SHARE- whole class review

A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

### Properties of Trapezoids

Consecutive angles between the bases

are supplementary.

Base angles of isosceles trapezoids

are congruent.

⦟P  ⦟S and ⦟Q  ⦟R

### if a quadrilateral is a parallelogram

• opposite sides are parallel (DEFINITION)

• opposite sides are congruent

• opposite angles are congruent

• consecutive angles are supplementary

• diagonals bisect each other

### Rhombus Properties

Rhombuses share all properties of a parallelogram

AND:

(1) Consecutive sides of a rhombus are congruent.

(2) The diagonals of a rhombus bisect pairs

of opposite angles.

(3) The diagonals of a rhombus are perpendicular.

### Rectangle Properties

All properties of a parallelogram AND:

• Diagonals are congruent

• All angles are congruent (90⁰)

### deductive reasoning

the process of showing that certain statements follow logically from agreed-upon assumptions and proven facts.

Inductive reasoning allows you to discover new ideas based on observed patterns.

Deductive reasoning can help explain

### Got Proof?

Logically step by step– what is true? why?

statement  reason

THREE styles- flowchart, two-column, paragraph

Let’s practice–

Complete Geometry Proof Practice Handout

FIRST- MARK the diagram with GIVEN information and HIDDEN congruencies!!

### WHOLE CLASS

• Complete Properties of Polygons Handout

SKETCHES and Conjectures

for Parallelograms

FINISHED? do the proof on the back

### Debrief

What is easy?

What still might be confusing to some students?

### Geometry 28 January 2014

WARM UP- on your pink sheet

• Find m⦟T 2)

FINISHED?

Work on geometry

Proof Practice

### Objective

Students will be able to prove and apply polygon properties.

HOMEWORK- DUE FRIDAY

pg. 283: 1 – 6; pg. 304: 7 – 12; pg. 300: 1, 3, 4

Properties of Parallelograms Handout

UNIT 5 TEST- FRIDAY We will NOT have time to go over homework questions before the test.

ANSWERS will be posted Wed/Th– see me w/ ?’s

a) 5b) 24 c) 48

What is x?

### Review 2

In a rectangle ABCD, if AB = 7x – 3, and CD = 4x + 9, then x = ___ (strategy– draw a sketch)

A) 1

B) 2

C) 3

D) 4

E) 5

7x – 3 = 4x + 9

-4x -4x

3x – 3 = 9

+ 3 +3

3x = 12

x = 4

### Review 3

• The perimeter of a square MNOP is 72 inches, and NO = 2x + 6. What is the value of x?

A) 15

B) 12

C) 6

D) 9

E) 18

FLOW CHART PROOF

1. Restate given information clearly.

Mark the information on a sketch.

Write the given information on the left.

2. State what you are trying to show.

3. Fill in the other boxes working backwards and forwards as needed.

4. ARROWS are used to connect information directly resulting from a previous statements.

Thinking FLOWS left to right.

1.

Given: parallelogram SOAK with diagonal

Show:

Def. of parallelogram

AIA

SOAK is a parallelogram

ASA

GIVEN

AIA

Def of

parallelogram

same segment

### KHAN Quiz

FINISHED? Work on Geometry Proof Practice

FINISHED? Work on 5.3 et. al. handout

### Debrief

What is easy?

What might still be confusing to some students?

### Geometry 29/ 30 January 2014

EMPTY Group Folders

• Look over your work from last week on the “Four Pentagons” Problem

• Correct or finish your work as needed

Please RESPOND to the prompts I wrote on your paper. You may use the 2nd clean sheet to re-work the problem as needed.

FINISHED? DO HW pblm pg. 300, #4.

### Objective

Students will be able to prove and apply polygon properties.

HOMEWORK- DUE FRIDAY

pg. 283: 1 – 6; pg. 304: 7 – 12; pg. 300: 1, 3, 4

Properties of Parallelograms Handout

UNIT 5 TEST- FRIDAY We will NOT have time to go over homework questions before the test.

ANSWERS will be posted Wed/Th– see me w/ ?’s

### Review Chapter 5 Quiz 2

What errors did you make?

CORRECTONS for up to ½ credit accepted through February 6. Follow pink slip guidelines!

DISCUSS-

Parallelogram Proofs on Geometry Proof Practice

REVIEW- Khan Quiz from yesterday

### PQRS is an isosceles trapezoid. Find m<P, m<Q, and m<R.

S

R

>

50°

>

P

Q

base angles are congruent

m<R= 50⁰

consecutive angles are

supplementary

m<Q=m<P= 180 – 50 = 130º

check: 2(50) + 2(130) = 100 + 260 = 360√

REVIEW 1

a =

x=

y=

• Find m<A

A) 65°

B) 135°

C) 100°

D) 90°

E) 105°

B

A

165°

C

30°

65°

D

### Review 3

• Opposite angles of a parallelogram must be _______.

A) complementary

B) supplementary

C) congruent

D) A and C

E) B and C

### Review 4

• If a quadrilateral has four equal sides, then it must be a _______.

A) rectangle

B) square

C) rhombus

D) A and B

E) B and C

### Review 5

• The perimeter of a square MNOP is 96 inches, and NO = 2x + 6. What is the value of x?

A) 15

B) 12

C) 9

D) 6

E) 3

### Review 6

• ABCD is a trapezoid. Find the length of midsegment EF.

A) 5

B) 11

C) 16

D) 8

E) 22

13

A

E

11

B

5

D

F

C

9

### Review 7

• The quadrilateral below is most specifically a __________.

A) rhombus

B) rectangle

C) kite

D) parallelogram

E) trapezoid

Mark/ briefly summarize properties of each quadrilateral on handout. REMEMBER- each shape has ALL the properties of the classification above it.

Kite

Parallelogram

Trapezoid

Isosceles Trapezoid

Rhombus

Rectangle

Square

### Let’s PRACTICE

COMPLETE 5.3 Handout for classwork.

FINISHED? Begin Instructional Task: Applying Angle Theorems- Four Pentagons

### Debrief

What do you need to do to be ready for the test on Friday?

### Geometry Unit 5 TEST31 January 2014

Do you best.

Work silently.

You have the whole period to

complete the test.

SHOW supporting work for

ALL PROBLEMS!!!

HOMEWORK DUE SUNDAY- KHAN ASSIGNMENT

### TEST postponed due to low attendance

HOMEWORK QUESTIONS?

Polygon Properties Practice-

Practice Handout

White Board Review