Teach on Udemy

Turn what you know into an opportunity and reach millions around the world.

Learn More

Your cart is empty.

Keep shopping

Become A Master of Geometry - Triangles

High school math that covers Geometry - Triangles in detail, with a step-by-step approach with theorem and proofs.

Created byLakshmi Narayana

Last updated 11/2022

English

What you'll learn

Similarities: Similar Figures, Similar Polygons, and Similar Triangles
Basic Proportionality Theorem (BPT) or Thales Theorem and its applications.
Applications of the Converse Basic Proportionality Theorem.
Criteria for Similarity of Triangles and Related Proofs: AAA Similarity Criteria, SSS Similarity Criterion, and SAS Similarity Criterion.
Areas of Similar Triangles and Their Applications.
Pythagoras' Theorem and its Applications.
Converse of Pythagoras' Theorem and its Applications.
At the end of the course, students will not only have learned about the topics in detail but also be able to solve various problems based on them.

Course content

15 sections • 112 lectures • 12h 57m total length

Introduction9:34
Introduction:
In previous class, we have studied about congruent figures. We know that two figures are called congruent, if they have the same shape and the same size. In this chapter, we shall study about those figures which are in same shape but not necessarily in the same size.
Q 15:14
In Figure, if ∆ABC ~ ∆DEF and their sides are of lengths (in cm)
as marked along them, then find the lengths of the sides of each triangle.
Q 24:25
In the given figure, △ABC △PQR. Find the value of y + z.
Q 34:04
If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E,
then which of the following is not true?
i. EF/PR = DF/PQ
ii. DE/PQ = EF/RP
iii. DE/QR = DF/PQ
iv. EF/RP = DE/QR
Q 46:39
It is given that ABC ~ DFE, A = 30°, C = 50°, AB = 5cm,
AC = 8 cm and DF= 7.5 cm. Then, the following is true:
1) DE = 12 cm, F = 50°
2) DE = 12 cm, F = 100°
3) EF = 12 cm, D = 100°
4) EF = 12 cm, D = 30°
Test your understanding
Home Assignment

Introduction12:36
Basic Proportionality Theorem (BPT)& Its applications.
Q 14:57
If a line intersects sides AB and AC of a ∆ABC at D and E respectively and is parallel to BC, prove that (AD )/AB = (AE )/AC.
Q 26:32
ABCD is a trapezium with AB || DC. E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB. Show that AE/ED = BF/FC
Q 34:37
In Fig. DE∥BC and CD∥EF. Prove that AD^2 = AB × AF.
Q 47:29
In △ABC, D and E are points on the sides AB and AC respectively, such that DE || BC. If AD = 4x - 3, AE = 8x - 7, BD = 3x - 1 and CE = 5x -3 , find the value of x.
Test your understanding
Home Assignment

Introduction7:36
Converse of Basic Proportionality Theorem & its applications.
Q 15:38
In figure, = and PST = PRQ. Prove that PQR is an isosceles triangle.
Q 24:30
If the diagonals of a quadrilateral divide each other proportionally, prove that it is a trapezium.
Q 35:52
In the given figure, ∠A = ∠B and AD = BE. Show that DE ∥ AB.
Q 43:09
If D and E are points on the respective sides AB and AC. △ABC such that, AD = 6 cm, BD = 9 cm, AE = 8 cm,
EC = 12 cm. Prove that DE || BC.
Test your understanding
Home Assignment

Introduction1:59
Criteria for Similarity of Triangles & related proofs.
· AAA Similarity Criterion
· SSS Similarity Criterion
· SAS Similarity Criterion
Problems Based on Similarity of Triangles
Theorem 110:19
AAA Similarity Criterion:
If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio(or proportion) and hence the two triangles are similar.
Theorem 29:31
SSS Similarity Criterion:
If in two triangles, sides of one triangle are proportional to (i.e. in the same ratio ) to the side of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.
Theorem 36:39
SAS Similarity Criterion:
If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then two triangles are similar.
Q 12:53
In the adjoining figure, △AHK is similar to △ABC.
If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find AC.
Q 24:29
Observe the figure and then find ∠P.
Q 37:22
A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.
Test your understanding
Home Assignment

Introduction2:40
Proofs Based on Similarity of Triangles
Q 13:35
In figure, if PQ || RS, prove that ∆POQ ~ ∆SOR.
Q 23:50
In figure, OA. OB = OC. OD. Show that ∠A = ∠C and ∠B = ∠D.
Q 313:42
In figure, CM and RN are respectively the medians of ∆ABC and ∆PQR. If ∆ABC ~ ∆PQR, prove that:
i. ∆AMC ~ ∆PNR
ii. (CM )/RN =(AB )/PQ
iii. ∆CMB ~ ∆RNQ
Q 46:45
In the given figure, AB ∥ PQ ∥ CD, AB = x, CD = y, PQ = z
Prove that (1 )/(x ) + (1 )/(y ) = (1 )/(z )
Test your understanding
Home Assignment

Introduction9:53
Areas of Similar Triangles&
Problems Based on Areas of Similar Triangles
Q 18:31
In figure, the line segment XY is parallel to side AC of ∆ABC and it divides the triangle into two parts of equal areas. Find the ratio AX/AB
Q 26:51
In the given figure, PA/AQ = PB/BR = 3. If the area △PQR is 32 cm^2,
then find the area of the quadrilateral AQRB.
Q 32:56
ΔABC and ΔDEF are similar and AB = (1/3)DE,
then find ar(ΔABC): ar(ΔDEF)
Q 410:42
In the given figure, if DE∥BC and AD : DB = 5 : 4, then find (ar(△DFE) )/(ar(△CFB) )
Test your understanding
Home Assignment

Introduction1:22
Areas of Similar Triangles
&
Proofs Based on Areas of Similar Triangles
Q 14:17
If △ABC ∼ △PQR and AD and PS are bisectors of corresponding angles A and P, then prove that
(ar(ΔABC) )/(ar(ΔPQR)) = AD^2/PS^2 .
Q 23:37
If the area of two similar triangles are equal, prove that they are congruent.
Q 33:55
Diagonals of a trapezium PQRS intersect each other at the point O, PQ ∥ RS and PQ = 3RS. Find the ratio of the areas of triangles △POQ and △ROS.
Q 44:16
Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.
Test your understanding
Home Assignment

Introduction6:35
Pythagoras Theorem and its Applications.
Q 15:42
In figure, ∠ACB = 900 and CD⊥ AB. Prove that (BC^2)/(AC^2 ) = BD/AD
Q 23:56
In figure, if AD⊥ BC, prove that AB^2 + CD^2 = BD^2 + AC^2.
Q 35:24
BL and CM are medians of a triangle ABC right angled at A.
Prove that4(BL^2 + CM^2) = 5BC^2
Q 43:12
A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.
Test your understanding
Home Assignment

Introduction7:56
Proofs Based on Converse of Pythagoras Theorem:
Q 15:55
O is any point inside a rectangle ABCD.
Prove that OB^2 + OD^2 = OA^2 + OC^2.
Q 28:21
ΔABC is right angled at C. If p is the length of the perpendicular from C to AB and a, b, c are the lengths of the sides opposite ∠A, ∠B and ∠C respectively, then prove that 1/P^2 = 1/a^2 + 1/b^2
Q 36:44
In a ΔABC, AD⊥BC and AD^2 = BD × CD.
Prove that ΔABC is a right triangle.
Q 44:13
In an equilateral triangle of side √3 cm,
find the length of the altitude.
Test your understanding
Home Assignment

Q 14:16
Fill in the blanks using the correct word given in brackets :
(i) All circles are_______. (congruent, similar)
(ii) All squares are __________. (similar, congruent)
(iii) All _______ triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if
(a) their corresponding angles are _________ and
(b) their corresponding sides are _________. (equal, proportional)
Q 22:44
Give two different examples of pair of
(i) Similar figures. (ii) Non-similar figures.
Q 32:01
State whether the following quadrilaterals are similar or not

Requirements

Elementary knowledge of basic geometry.
Elementary knowledge of middle school math.
Each chapter is inbuilt with prerequisite knowledge classes where the child gets immense knowledge and a clear understanding of the chapters.

Description

This course is carefully designed to explain various topics in Geometry - Triangles
It has 112 lectures spanning around thirteen hours of on-demand videos that are divided into 9 sessions. The course is divided into a simplified day-by-day learning schedule.
Each topic is divided into simple sessions and explained extensively by solving multiple questions. Each session contains a detailed explanation of the concept.
An online test related to the concept for immediate assessment of understanding.
Session-based daily home assignments with a separate key The students are encouraged to solve practice questions and quizzes provided at the end of each session.
This course will give you a firm understanding of the fundamentals and is designed in a way that a person with little or no previous knowledge can also understand very well.
It covers 100% video solutions of the NCERT exercises , with selected NCERT exemplars and R D Sharma.
Our design meets the real classroom experience by following classroom teaching practices. We have designed this course by keeping in mind all the needs of students and their desire to become masters in math. This course is designed to benefit all levels of learners and will be the best gift for board-appearing students. Students love these easy methods and explanations. They enjoy learning maths and never feel that maths is troublesome.

Topics covered in the course:

Similarities:
- Similar Figures
- Similar Polygons
- Similar Triangles
- Basic Proportionality Theorem (BPT) or Thales Theorem and it applications.
Applications of Converse of Basic Proportionality Theorem.
Criteria for Similarity of Triangles & related proofs.
- AAA Similarity Criterion
- SSS Similarity Criterion
- SAS Similarity Criterion
Areas of Similar Triangles & its applications.
Pythagoras Theorem and its Applications.
Converse of Pythagoras Theorem and its Applications.

With this course you'll also get:

Perfect your mathematical skills on Geometry - Triangles.
A Udemy Certificate of Completion is available for download.

Feel free to contact me with any questions or clarifications you might have.

I can't wait for you to get started on mastering the real number systems.

I look forward to seeing you on the course! :)

Benefits of Taking this Course:

On completion of this course, one will have detailed knowledge of the chapter and be able to easily solve all the problems, which can lead to scoring well in exams with the help of explanatory videos ensure complete concept understanding.

Downloadable resources help in applying your knowledge to solve various problems.

Quizzes help in testing your knowledge. In short, one can excel in math by taking this course.

Who this course is for:

This course has been designed for students of the Grade 10th CBSE, ICSE, SSC, GCSE, IGCSE, SAT, ACT, GRE, and other board-appearing students.
Students studying for the public or other competitive examinations
Home-school parents are looking for extra support with the fundamentals.
Anyone interested in revising or learning the basics of mathematics should.
Students in junior high and high school/secondary schools.
Anyone who wants to proficient mathematics and the Algebra – Arithmetic Progressions well.
Anyone who wants to study math for fun after taking a break from school.
It will also benefit schools who wish to run classes in the absence of a teacher and make learning fun for their students.
It will also benefit teachers and schools who wish to improve their teaching skills and make learning fun for their students.
For 11th, 9th, and 8th grade students, this will help as a bridge course.

Become A Master of Geometry - Triangles

What you'll learn

Explore related topics

Course content

Session 15 lectures • 30min

Session 25 lectures • 36min

Session 35 lectures • 27min

Session 47 lectures • 43min

Session 55 lectures • 31min

Session 65 lectures • 39min

Session 75 lectures • 17min

Session 85 lectures • 25min

Session 95 lectures • 33min

Exercise 6.13 lectures • 9min

Requirements

Description

Who this course is for: