This was our written report in Modern Geometry :) I hope that this will be helpful to other students since we had a very difficult time in searching for references.
This was our written report in Modern Geometry :) I hope that this will be helpful to other students since we had a very difficult time in searching for references.
Thses slides will explain you the prperties of the of parallelograms. how to draw the parallelogram and how to determine the properties of paralleograms. Thses slides having the large number of examples to show the properties.
Thses slides will explain you the prperties of the of parallelograms. how to draw the parallelogram and how to determine the properties of paralleograms. Thses slides having the large number of examples to show the properties.
A plane figure with three sides and three angles is called a triangle. We will learn the different types of triangles based on varying side lengths and angle measurements. After this session you can very easily tell the difference between all types of triangles and know the mathematics involved in it.
Did you know, two different triangles of different sizes can be similar to each other based on the ratio of their sides ?
Here you will learn the following:
1) Criteria’s for similarity
2) Scale factor
3) Congruency
If the corresponding sides of a triangle is twice than that of another triangle, will the area be also doubled??
Watch this session to learn about the effects that can be seen in areas of two similar triangles in just 10 minutes.
Basic Proportionality Theorem is one of the important topics of a Triangle that deals with the study of the proportion of the two sides of a triangle. So, watch this session and learn about the Theorem and its proof.
Pythagoras theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
In this session, you will learn this very important theorem and learn to prove its statement with its proof in a geometric way.
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Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
2. Essential Questions
How do you recognize and apply properties of the sides and
angles of parallelograms?
How do you recognize and apply properties of the diagonals of
parallelograms?
5. Properties and Theorems
6.3 - Opposite Sides:
6.4 - Opposite Angles:
6.5 - Consecutive Angles:
6.6 - Right Angles:
6. Properties and Theorems
6.3 - Opposite Sides: If a quadrilateral is a parallelogram, then its
opposite sides are congruent
6.4 - Opposite Angles:
6.5 - Consecutive Angles:
6.6 - Right Angles:
7. Properties and Theorems
6.3 - Opposite Sides: If a quadrilateral is a parallelogram, then its
opposite sides are congruent
6.4 - Opposite Angles: If a quadrilateral is a parallelogram, then its
opposite angles are congruent
6.5 - Consecutive Angles:
6.6 - Right Angles:
8. Properties and Theorems
6.3 - Opposite Sides: If a quadrilateral is a parallelogram, then its
opposite sides are congruent
6.4 - Opposite Angles: If a quadrilateral is a parallelogram, then its
opposite angles are congruent
6.5 - Consecutive Angles: If a quadrilateral is a parallelogram, then its
consecutive angles are supplementary
6.6 - Right Angles:
9. Properties and Theorems
6.3 - Opposite Sides: If a quadrilateral is a parallelogram, then its
opposite sides are congruent
6.4 - Opposite Angles: If a quadrilateral is a parallelogram, then its
opposite angles are congruent
6.5 - Consecutive Angles: If a quadrilateral is a parallelogram, then its
consecutive angles are supplementary
6.6 - Right Angles: If a parallelogram has one right angle, then it has four
right angles
11. Properties and Theorems
6.7 - Bisecting Diagonals: If a quadrilateral is a parallelogram, then its
diagonals bisect each other
6.8 - Triangles from Diagonals:
12. Properties and Theorems
6.7 - Bisecting Diagonals: If a quadrilateral is a parallelogram, then its
diagonals bisect each other
6.8 - Triangles from Diagonals: If a quadrilateral is a parallelogram, then
each diagonal separates the parallelogram into two congruent
triangles
13. Example 1
In ABCD, suppose m∠B = 32°, CD = 80 inches, and BC = 15 inches.
Find each measure.
a. AD
b. m∠C
c. m∠D
14. Example 1
In ABCD, suppose m∠B = 32°, CD = 80 inches, and BC = 15 inches.
Find each measure.
a. AD 15 inches
b. m∠C
c. m∠D
15. Example 1
In ABCD, suppose m∠B = 32°, CD = 80 inches, and BC = 15 inches.
Find each measure.
a. AD 15 inches
b. m∠C = 180 − 32
c. m∠D
16. Example 1
In ABCD, suppose m∠B = 32°, CD = 80 inches, and BC = 15 inches.
Find each measure.
a. AD 15 inches
b. m∠C = 180 − 32 = 148°
c. m∠D
17. Example 1
In ABCD, suppose m∠B = 32°, CD = 80 inches, and BC = 15 inches.
Find each measure.
a. AD 15 inches
b. m∠C = 180 − 32 = 148°
c. m∠D = 32°
18. Example 2
If WXYZ is a parallelogram, find the value of the indicated variable.
m∠VWX = (2t)°, m∠VYX = 40°, m∠VYZ =18°,
WX = 4r, ZV = 8s, VX = 7s + 3, ZY =18
a. r b. s
c. t
19. Example 2
If WXYZ is a parallelogram, find the value of the indicated variable.
m∠VWX = (2t)°, m∠VYX = 40°, m∠VYZ =18°,
WX = 4r, ZV = 8s, VX = 7s + 3, ZY =18
a. r
WX = ZY
b. s
c. t
20. Example 2
If WXYZ is a parallelogram, find the value of the indicated variable.
m∠VWX = (2t)°, m∠VYX = 40°, m∠VYZ =18°,
WX = 4r, ZV = 8s, VX = 7s + 3, ZY =18
a. r
WX = ZY
4r = 18
b. s
c. t
21. Example 2
If WXYZ is a parallelogram, find the value of the indicated variable.
m∠VWX = (2t)°, m∠VYX = 40°, m∠VYZ =18°,
WX = 4r, ZV = 8s, VX = 7s + 3, ZY =18
a. r
WX = ZY
4r = 18
r = 4.5
b. s
c. t
22. Example 2
If WXYZ is a parallelogram, find the value of the indicated variable.
m∠VWX = (2t)°, m∠VYX = 40°, m∠VYZ =18°,
WX = 4r, ZV = 8s, VX = 7s + 3, ZY =18
a. r
WX = ZY
4r = 18
r = 4.5
b. s
ZV = VX c. t
23. Example 2
If WXYZ is a parallelogram, find the value of the indicated variable.
m∠VWX = (2t)°, m∠VYX = 40°, m∠VYZ =18°,
WX = 4r, ZV = 8s, VX = 7s + 3, ZY =18
a. r
WX = ZY
4r = 18
r = 4.5
b. s
ZV = VX
8s = 7s + 3
c. t
24. Example 2
If WXYZ is a parallelogram, find the value of the indicated variable.
m∠VWX = (2t)°, m∠VYX = 40°, m∠VYZ =18°,
WX = 4r, ZV = 8s, VX = 7s + 3, ZY =18
a. r
WX = ZY
4r = 18
r = 4.5
b. s
ZV = VX
8s = 7s + 3
s = 3
c. t
25. Example 2
If WXYZ is a parallelogram, find the value of the indicated variable.
m∠VWX = (2t)°, m∠VYX = 40°, m∠VYZ =18°,
WX = 4r, ZV = 8s, VX = 7s + 3, ZY =18
a. r
WX = ZY
4r = 18
r = 4.5
b. s
ZV = VX
8s = 7s + 3
s = 3
c. t
m∠VWX = m∠VYZ
26. Example 2
If WXYZ is a parallelogram, find the value of the indicated variable.
m∠VWX = (2t)°, m∠VYX = 40°, m∠VYZ =18°,
WX = 4r, ZV = 8s, VX = 7s + 3, ZY =18
a. r
WX = ZY
4r = 18
r = 4.5
b. s
ZV = VX
8s = 7s + 3
s = 3
c. t
m∠VWX = m∠VYZ
2t = 18
27. Example 2
If WXYZ is a parallelogram, find the value of the indicated variable.
m∠VWX = (2t)°, m∠VYX = 40°, m∠VYZ =18°,
WX = 4r, ZV = 8s, VX = 7s + 3, ZY =18
a. r
WX = ZY
4r = 18
r = 4.5
b. s
ZV = VX
8s = 7s + 3
s = 3
c. t
m∠VWX = m∠VYZ
2t = 18 t = 9
28. Example 3
What are the coordinates of the intersection of the diagonals of
parallelogram MNPR with vertices M(−3, 0), N(−1, 3), P(5, 4) , and R(3, 1)?
29. Example 3
What are the coordinates of the intersection of the diagonals of
parallelogram MNPR with vertices M(−3, 0), N(−1, 3), P(5, 4) , and R(3, 1)?
M =
x1
+ x2
2
,
y1
+ y2
2
⎛
⎝
⎜
⎞
⎠
⎟
30. Example 3
What are the coordinates of the intersection of the diagonals of
parallelogram MNPR with vertices M(−3, 0), N(−1, 3), P(5, 4) , and R(3, 1)?
M =
x1
+ x2
2
,
y1
+ y2
2
⎛
⎝
⎜
⎞
⎠
⎟
M(MP) =
−3+ 5
2
,
0 + 4
2
⎛
⎝⎜
⎞
⎠⎟
31. Example 3
What are the coordinates of the intersection of the diagonals of
parallelogram MNPR with vertices M(−3, 0), N(−1, 3), P(5, 4) , and R(3, 1)?
M =
x1
+ x2
2
,
y1
+ y2
2
⎛
⎝
⎜
⎞
⎠
⎟
M(MP) =
−3+ 5
2
,
0 + 4
2
⎛
⎝⎜
⎞
⎠⎟ =
2
2
,
4
2
⎛
⎝⎜
⎞
⎠⎟
32. Example 3
What are the coordinates of the intersection of the diagonals of
parallelogram MNPR with vertices M(−3, 0), N(−1, 3), P(5, 4) , and R(3, 1)?
M =
x1
+ x2
2
,
y1
+ y2
2
⎛
⎝
⎜
⎞
⎠
⎟
M(MP) =
−3+ 5
2
,
0 + 4
2
⎛
⎝⎜
⎞
⎠⎟ =
2
2
,
4
2
⎛
⎝⎜
⎞
⎠⎟ = 1,2( )
33. Example 3
What are the coordinates of the intersection of the diagonals of
parallelogram MNPR with vertices M(−3, 0), N(−1, 3), P(5, 4) , and R(3, 1)?
M =
x1
+ x2
2
,
y1
+ y2
2
⎛
⎝
⎜
⎞
⎠
⎟
M(MP) =
−3+ 5
2
,
0 + 4
2
⎛
⎝⎜
⎞
⎠⎟ =
2
2
,
4
2
⎛
⎝⎜
⎞
⎠⎟ = 1,2( )
M(NR) =
−1+ 3
2
,
3+1
2
⎛
⎝⎜
⎞
⎠⎟
34. Example 3
What are the coordinates of the intersection of the diagonals of
parallelogram MNPR with vertices M(−3, 0), N(−1, 3), P(5, 4) , and R(3, 1)?
M =
x1
+ x2
2
,
y1
+ y2
2
⎛
⎝
⎜
⎞
⎠
⎟
M(MP) =
−3+ 5
2
,
0 + 4
2
⎛
⎝⎜
⎞
⎠⎟ =
2
2
,
4
2
⎛
⎝⎜
⎞
⎠⎟ = 1,2( )
M(NR) =
−1+ 3
2
,
3+1
2
⎛
⎝⎜
⎞
⎠⎟ =
2
2
,
4
2
⎛
⎝⎜
⎞
⎠⎟
35. Example 3
What are the coordinates of the intersection of the diagonals of
parallelogram MNPR with vertices M(−3, 0), N(−1, 3), P(5, 4) , and R(3, 1)?
M =
x1
+ x2
2
,
y1
+ y2
2
⎛
⎝
⎜
⎞
⎠
⎟
M(MP) =
−3+ 5
2
,
0 + 4
2
⎛
⎝⎜
⎞
⎠⎟ =
2
2
,
4
2
⎛
⎝⎜
⎞
⎠⎟ = 1,2( )
M(NR) =
−1+ 3
2
,
3+1
2
⎛
⎝⎜
⎞
⎠⎟ =
2
2
,
4
2
⎛
⎝⎜
⎞
⎠⎟ = 1,2( )
36. Example 4
Given ABCD, AC and BD are diagonals, P is the intersection of AC
and BD, prove that AC and BD bisect each other.
37. Example 4
Given ABCD, AC and BD are diagonals, P is the intersection of AC
and BD, prove that AC and BD bisect each other.
1. ABCD is a parallelogram, AC and BD are diagonals,
P is the intersection of AC and BD
38. Example 4
Given ABCD, AC and BD are diagonals, P is the intersection of AC
and BD, prove that AC and BD bisect each other.
1. ABCD is a parallelogram, AC and BD are diagonals,
P is the intersection of AC and BD
1. Given
39. Example 4
Given ABCD, AC and BD are diagonals, P is the intersection of AC
and BD, prove that AC and BD bisect each other.
1. ABCD is a parallelogram, AC and BD are diagonals,
P is the intersection of AC and BD
1. Given
2. AB is parallel to CD
40. Example 4
Given ABCD, AC and BD are diagonals, P is the intersection of AC
and BD, prove that AC and BD bisect each other.
1. ABCD is a parallelogram, AC and BD are diagonals,
P is the intersection of AC and BD
1. Given
2. Definition of parallelogram2. AB is parallel to CD
41. Example 4
Given ABCD, AC and BD are diagonals, P is the intersection of AC
and BD, prove that AC and BD bisect each other.
1. ABCD is a parallelogram, AC and BD are diagonals,
P is the intersection of AC and BD
1. Given
2. Definition of parallelogram
3. ∠BAC ≅ ∠DCA, ∠BDC ≅ ∠DBA
2. AB is parallel to CD
42. Example 4
Given ABCD, AC and BD are diagonals, P is the intersection of AC
and BD, prove that AC and BD bisect each other.
1. ABCD is a parallelogram, AC and BD are diagonals,
P is the intersection of AC and BD
1. Given
2. Definition of parallelogram
3. ∠BAC ≅ ∠DCA, ∠BDC ≅ ∠DBA
2. AB is parallel to CD
3.Alt. int. ∠’s of parallel lines ≅
43. Example 4
Given ABCD, AC and BD are diagonals, P is the intersection of AC
and BD, prove that AC and BD bisect each other.
1. ABCD is a parallelogram, AC and BD are diagonals,
P is the intersection of AC and BD
1. Given
2. Definition of parallelogram
3. ∠BAC ≅ ∠DCA, ∠BDC ≅ ∠DBA
2. AB is parallel to CD
3.Alt. int. ∠’s of parallel lines ≅
4. AB ≅ CD
44. Example 4
Given ABCD, AC and BD are diagonals, P is the intersection of AC
and BD, prove that AC and BD bisect each other.
1. ABCD is a parallelogram, AC and BD are diagonals,
P is the intersection of AC and BD
1. Given
2. Definition of parallelogram
3. ∠BAC ≅ ∠DCA, ∠BDC ≅ ∠DBA
2. AB is parallel to CD
3.Alt. int. ∠’s of parallel lines ≅
4. AB ≅ CD 4. Opposite sides of parallelograms ≅
