congruent - identical in form

Formula: ≅

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the mea

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the measure of all 3 angles?
Let the congruent angles measurement be c. And the non-congruent angle measurement be n. We're given:
[LIST=1]
[*]n = 2c + 16 <-- Twice means we multiply by 2, and more than means we add 16
[*]2c + n = 180 <-- Since the sum of angles in an isosceles triangle is 180
[/LIST]
Substitute (1) into (2):
2c + (2c + 16) = 180
Group like terms:
4c + 16 = 180
[URL='https://www.mathcelebrity.com/1unk.php?num=4c%2B16%3D180&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]c = 41[/B]
Substituting this value into Equation 1, we get
n = 2(41) + 16
n = 82 + 16
[B]n = 98[/B]

C is the midpoint of BD then BC congruent CD

C is the midpoint of BD then BC congruent CD
[URL='https://www.mathcelebrity.com/proofs.php?num=cisthemidpointofbd&pl=Prove']True using this proof[/URL]

Congruence Modulo n

Free Congruence Modulo n Calculator - Given a possible congruence relation a ≡ b (mod n), this determines if the relation holds true (b is congruent to c modulo n).

Find x

Find x
[IMG]https://mathcelebrity.com/community/data/attachments/0/cong-angles.jpg[/IMG]
Since both angles are congruent, we set them equal to each other:
6x - 20 = 4x
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x-20%3D4x&pl=Solve']type this equation into our math engine[/URL] and we get:
x = [B]10[/B]

if two angles are supplementary and congruent then they are right angles

if two angles are supplementary and congruent then they are right angles
Let the first angle be x. Let the second angle be y.
Supplementary angles means their sum is 180:
x + y = 180
We're given both angles are congruent, meaning equal. So we set x = y:
y + y = 180
To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=y%2By%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
y = [B]90. <-- 90 degrees is a right angle, so this is TRUE[/B]

Linear Congruential Generator

Free Linear Congruential Generator Calculator - Using the linear congruential generator algorithm, this generates a list of random numbers based on your inputs

M is the midpoint of AB. Prove AB=2AM

M is the midpoint of AB. Prove AB=2AM
M is the midpoint of AB (Given)
AM = MB (Definition of Congruent Segments)
AM + MB = AB (Segment Addition Postulate)
AM + AM = AB (Substitution Property of Equality)
2AM = AB (Distributive property)

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is the area of one piece?
A pizza is a circle. If the diameter of the pizza is 14 inches, the radius is 14/2 = 7 inches.
Area of a circle is pi(r^2). With r = 7, we have:
A =7^2(pi)
A = 49pi
Area of a slice of pizza is the area of the full pizza divided by 8
A(Slice) = [B]49pi/8[/B]

n and m are congruent and supplementary. prove n and m are right angles

n and m are congruent and supplementary. prove n and m are right angles
Given:
[LIST]
[*]n and m are congruent
[*]n and m are supplementary
[/LIST]
If n and m are supplementary, that means we have the equation:
m + n = 180
We're also given n and m are congruent, meaning they are equal. So we can substitute n = m into the supplementary equation:
m + m = 180
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%3D180&pl=Solve']we type it in our search engine[/URL] and we get:
m = 90
This means m = 90, n = 90, which means they are both right angles since by definition, a right angle is 90 degrees.

rectangle abcd prove: triangle adc is congruent to triangle bcd

rectangle abcd prove: triangle adc is congruent to triangle bcd
1. Given: ABCD is a rectangle
2. AB = CD since opposite sides of rectangle are congruent
3. BC = AD since opposite sides of rectangle are congruent
4. AC = AC by the Reflexive Property of Equality
5. triangle ADC = triangle CBA by the Side-Side-Side (SSS) Property