Geometry & Math Apps

Week of:

APRIL 27TH WICHITA PUBLIC SCHOOLS

9th, 10th, 11th and 12th Grades

Your child should spend up to 90 minutes over the course of each day on this packet. Consider other family-friendly activities during the day such as:

Wash a car by hand with someone in your family.

Make a dish using a recipe that has at least

four ingredients.

Have a discussion regarding social

distancing with your family. What has been the

hardest part? What has been the easiest?

Go on a photo scavenger hunt. Try to find something that goes with each letter

of the alphabet.

Read a book from the free section of iBooks or gutenberg.org

Explore the power Hubble at

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Mindful Minute: Write a letter to your future self about what is going on

right now. How are you feeling?

Play a board game with you family.

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contact their child’s IEP manager, and/or speak to the special education provider when you are contacted by them. Contact the IEP manager by emailing them directly or by contacting the school.

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Congruent Triangles and CPCTC Congruent Triangles are the same shape and size. They have 3 pairs of corresponding congruent sides, and 3 pairs of corresponding congruent angles.

If ∆ABC ≅ ∆DEF

Then 𝐴𝐴𝐴𝐴���� ≅ 𝐷𝐷𝐷𝐷����, 𝐴𝐴𝐵𝐵���� ≅ 𝐷𝐷𝐸𝐸����, and 𝐴𝐴𝐵𝐵���� ≅ 𝐷𝐷𝐸𝐸���� are the 3 corresponding congruent sides,

And ∠A ≅ ∠D, ∠B ≅ ∠E, and ∠C ≅ ∠F are the 3 corresponding congruent angles

CPCPT – Corresponding Parts of Congruent Triangles are Congruent.

Means that once you prove triangles are congruent using SSS, SAS, ASA, AAS, or HL, you now know that all corresponding parts are congruent.

Used to prove Triangles Congruent Now known using CPCTC SSS The 3 angles (AAA) SAS The unused Side and the two unused angles (ASA) ASA The unused Angle and the two unused Sides (SAS) AAS The unused Angle and the two unused Sides (SSA) HL (ASS) The two non-right angles and the unused leg (SAA)

Example:

Triangles are congruent using SAS

Therefore we can use CPCPC to prove the remaining ASA

A - ∠K ≅ ∠N

S - 𝐾𝐾𝐾𝐾���� ≅ 𝑁𝑁𝐾𝐾����

A - ∠KLJ ≅ ∠NLM

A C

B E

F D

Geometry Name

CPCTC WORKSHEET Date Hour

#1: HEY is congruent to MAN by ______.

What other parts of the triangles are congruent by CPCTC?

______ ______

______ ______

______ ______

#2:

CAT ______, by _____

THEREFORE:

______ ______, by CPCTC

______ ______, by CPCTC

______ ______, by CPCTC

#3:

Given: ARAC and 21

Prove: 43

Proof:

1. ARAC

2. ____________

3. RASCAL

4. LCA SRA

5. 43

1. ____________

2. Given

3. ________________

4. ____________

5. __________

M

A

N

Y

E

H

L

C

S

R

4 3

2 1

C

T P

A

R

A

#4:

Given: LNONLM and MNLOLN

Prove: OM

Proof:

1. LNONLM

2. _________________

3. _________________

4. LMN ______

5. _________________

1. _________________

2. Given

3. Reflexive Property of

4. _________________

5. _________________

#5

Given: BCAC and BXAX

Prove: 1 2

Proof:

1. __________________________ 1. Given

2. __________________________ 2. Reflexive Prop. of Congruence

3. AXC _______ 3. ____________

4. ________________ 4. ____________

#6

Given: 1 2 and 3 4

Prove: ZWXY

Proof:

1. __________________________ 1. Given

2. XZXZ 2. ________________

3. XWZ _______ 3. ____________

4. ________________ 4. ____________

M

N O

L

C

X B A

1 2

4 3

W

X Y

Z

1

2 3

4

6.

__

__

__ _

_

__

__

__ _

_

4.

__ _

_

__

__

____

Quadrilateral Family Tree

Quadrilateral 4-sided polygon

Opposite sides parallel Opposite sides congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other

One pair opposite sides parallel Leg angles supplementary

Parallelogram

Trapezoid

Four right angles Diagonals are congruent

Rectangle

Four congruent sides Perpendicular diagonals Diagonals bisect opposite angles

Rhombus

All of the above

Square

Legs are congruent Base angles congruent Diagonals congruent

Isosceles Trapezoid

2 pairs adjacent congruent sides Opp. sides not congruent or parallel

Kite

Properties of Quadrilaterals

Property Parallel-ogram

Rectangle Rhombus Square Kite Trapezoid Isosceles Trapezoid

Opposite sides are parallel � � � �

Opposite sides are congruent � � � �

Opposite angles are congruent � � � �

Diagonals form two congruent triangles � � � �

Diagonals bisect other � � � �

Diagonals are congruent � � �

Diagonals are perpendicular � � �

Diagonals bisect opposite angles � �

All angles are right angles � �

All sides are congruent � �

Consecutive angles are supplementary � � � �

Two pairs of consecutive congruent sides � � �

Opposite sides are not congruent or parallel �

Base sides are parallel � �

Legs are congruent �

Base angles are congruent �

Quadrilateral

Rectangle

Parallelogram

Square Rhombus

Trapezoid

Isosceles Trapezoid Kite

Parallelogram Proofs! Name ________________________ 5 Ways of Showing that a Quadrilateral is a Parallelogram: •

• • • •

1. Use the diagram at the right to prove the following theorem:

“If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.”

Given: Prove: Statements Reasons

1.

2. M is the midpoint of _____; M is the midpoint of ______ 3.

4. ∠AMB ≅ ∠CMD; ∠_________ ≅ ∠__________

5. ΔAMB ≅ Δ________; Δ_________ ≅ Δ________

6. 7. ABCD is a parallelogram

1.

2. Def. of segment bisector 3. Def. of midpoint

4. 5.

6. CPCTC 7. If both pairs of opp. sides of a quad. are ≅, then the quad. is a parallelogram

2. Given: Parallelogram ABCD; M and N are midpoints of

�

AB and

�

DC Prove: AMCN is a parallelogram Statements Reasons

1. 2.

�

AB ||DC (so

�

AM ||NC) 3.

�

AB ≅ DC , or AB = DC

4.

�

12AB =

12DC

5.

�

AM =12AB ;

�

NC =12DC

6. AM = NC, or

�

AM ≅ NC 7.

1.

2.

3.

4.

5.

6.

7.

(which one of these is the def. of parallelogram?)

3. Given: Parallelogram GHJK Prove: ΔGLH ≅ ΔJLK Statements Reasons

4. Given: FGHJ is a parallelogram; FK = HL Prove: KGLJ is a parallelogram Statements Reasons

1. FGHJ is a parallelogram

2.

�

JG and

�

FH bisect each other

3. O is the midpoint of

�

JG and

�

FH

4. FO = OH

5. FO = FK + KO; OH = ________________

6.

7. FK = HL

8. KO = OL

9. O is the midpoint of

�

KL

10.

11.

1.

2.

3.

4.

5.

6. Substitution

7. Given

8.

9.

10. Def. of segment bisector

11.

Geometry Support for Specialized Instruction

Monday CPCTC 1-4 Tuesday CPCTC 5-6, congruent triangle proof 1 WednesdayCongruent Triangle Proof 2 Thursday Parallelogram Proofs 1-2 Friday Parallelogram Proofs 3-4

If both pairs of opposite sides of a quadrilateral are parallel, the quadrilateral is a parallelogram. 2. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. 3. If one pair of opposite sides of a quadrilateral are both parallel and congruent, the quadrilateral is a parallelogram. 4. If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram. 5. If both pairs of opposite angles of a quadrilateral are congruent, the quadrilateral is a parallelogram. 6. If every pair of adjacent angles of a quadrilateral are supplementary, the quadrilateral is a parallelogram.