Subscribe to our YouTube channel for the latest videos, updates, and tips.
Right Angle Hypotenuse Side congruence
Conditions for the RHS - Right Angle Hypotenuse Side congruence
Two triangles triangle are congruent if the hypotenuse and one side of the one triangle are respectively equal to the hypotenuse and one side of the other.
Experiment to prove Congruence with RHS:
Draw a ∆LMN with ∠M = 90°, LM = 3cm LN = 5 cm,
Also, draw another ∆XYZ with ∠Y = 90°, XY = 3cm and XZ =
5cm.
We see that ∠M = ∠Y, LM = XY and LN = XZ.
Make a trace copy of ∆XYZ and try to make it cover ∆LMN with X on L, Y on M and Z on N.
We observe that: Two triangles cover each other exactly.
Therefore, ∆LMN ≅ ∆XYZ
Worked-out problems on right angle hypotenuse side congruence triangles (HL postulate):
1. ∆PQR is an isosceles triangle such that PQ = PR, prove that the altitude PO from P on QR bisects PQ.
Solution:
In the right triangles POQ and POR,
∠POQ = ∠POR = 90°
PQ = PR [since, ∆PQR is an isosceles. Given PQ = PR]
PO = OP [common]
Therefore ∆ POQ ≅ ∆ POR by RHS congruence condition
So, QO = RO (by corresponding parts of congruence triangles)
2. ∆XYZ is an isosceles triangle such that XY = XZ, prove that the altitude XO from X on YZ bisects YZ.
Solution:
In the right triangles XOY and XOZ,
∠XOY = ∠XOZ = 90°
XY = XZ [since, ∆XYZ is an isosceles. Given XY = XZ]
XO = OX [common]
Therefore ∆ XOY ≅ ∆ XOZ by RHS congruence condition
So, YO = ZO (by corresponding parts of congruence triangles)
3. In the adjoining figure, given that AB = BC, YB = BZ, BA ⊥ XY and BC ⊥ XZ. Prove that XY = XZ
Solution:
In right triangles YAB and BCZ we get,
YB = BZ [given]
AB = BC [given]
So, by RHS congruence condition
∆ YAB ≅ ∆ BCZ
∠Y = ∠Z (since by corresponding parts of congruence triangles are equal)
XZ = XY (since sides opposite to equal angles are equal)
Conditions for the Congruence of Triangles
Right Angle Hypotenuse Side congruence
Converse of Pythagorean Theorem
7th Grade Math Problems
8th Grade Math Practice
From Right Angle Hypotenuse Side congruence to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Speed Distance and Time | Relation between Speed Distance and Time
May 21, 25 12:58 PM
Speed is defined as the distance covered per unit time. Speed = (Distance Travelled)/(Time Taken) Or, S = D/T. Speed also requires a unit of measurement. If the distance is in kilometres -
Math Problem Answers | Solved Math Questions and Answers | Free Math
May 21, 25 12:45 PM
Math problem answers are solved here step-by-step to keep the explanation clear to the students. In Math-Only-Math you'll find abundant selection of all types of math questions for all the grades -
Test of Divisibility | Divisibility Rules| Divisible by 2, 3, 5, 9, 10
May 21, 25 10:29 AM
The test of divisibility by a number ‘x’ is a short-cut method to detect whether a particular number ‘y’ is divisible by the number ‘x’ or not. Test of divisibility by 2: A number is divisible by 2 -
Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7
May 21, 25 10:17 AM
Divisible by 7 is discussed below: We need to double the last digit of the number and then subtract it from the remaining number. If the result is divisible by 7, then the original number will also be -
Average Word Problems | Worksheet on Average Questions with Answers
May 20, 25 05:40 PM
In average word problems we will solve different types of problems on basic concept of average. 1. Richard scored 80, 53, 19, 77, 29 and 96 runs in 6 innings in a series. Find the average runs scored…
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.