Which postulate or theorem proves that these two triangles are congruent?
AAS Congruence Theorem
SAS Congruence Postulate
ASA Congruence Postulate
HL Congruence Theorem
Answers
From the figure,
JHGF is a parallelogram.
From the properties of parallelogram,
∠ F = ∠ H (opposite angles are equal)
FG = JH (opposite sides are equal)
Also, note that FG || JH and JG is a transversal.
Therefore,
∠ FGJ = ∠ GJH (Alternate interior angles are equal)
Now, in Δ FGJ and Δ GJH,
FG = JH
∠ F = ∠ H and
∠ FGJ = ∠ GJH
Hence, the triangles are congruent by AAS Congruence Theorem.
The triangles [tex]\triangle \text{FJG}[/tex] and [tex]\triangle \text{JHG}[/tex] are congruent by [tex]\fbox{\begin\\\ \bf {AAS congruence theorem}\\\end{minispace}}[/tex].
Further explanation:
From the given figure it is observed that there are two triangles [tex]\triangle \text{FJG}[/tex] and [tex]\triangle \text{JHG}[/tex] inside the quadrilateral.
Two triangles are said to be congruent if both the triangles have same angles and sides or it can be said that two triangles are congruent if they completely overlap with each other.
The theorems to check the congruency for the two triangles are as follows:
1) SSS congruence theorem:
As per the SSS congruence theorem if all the three sides of the first triangle are equal to all the three sides of the second triangle then the two triangles are called congruent triangles.
2) SAS congruence theorem:
As per the SAS congruence theorem if the two sides of first triangle are equal to the two sides of the second triangle and the including angles are equal then the two triangles are called congruent triangles.
3) AAS congruence rule:
As per the AAS congruence theorem if the two angles of first triangle are equal to the two angles of the second triangle and the similarly located sides are equal then the two triangles are called congruent triangles.
4) HL congruence rule:
As per the HL congruence theorem if the hypotenuse and the one other side of a triangle is equal to the hypotenuse and the corresponding other side of the second triangle then the two triangles are called congruent triangles.
From the given figure it is observed that [tex]\angle \text{GJH}[/tex] is equal to the [tex]\angle \text{JGF}[/tex], [tex]\angle \text{GHJ}[/tex] is equal to the [tex]\angle \text{GFJ}[/tex] and the side JG is the common side for [tex]\triangle \text{FJG}[/tex] and [tex]\triangle \text{JHG}[/tex].
From figure 1 (attached in the end) it is observed that the [tex]\angle \text{GJH}[/tex] and the [tex]\angle \text{JGF}[/tex] lies on same side, [tex]\angle \text{GHJ}[/tex] and the [tex]\angle \text{GFJ}[/tex] lies on the same side and the side JG is common for the [tex]\triangle \text{FJG}[/tex] and [tex]\triangle \text{JHG}[/tex].
For triangles [tex]\triangle \text{FJG}[/tex] and [tex]\triangle \text{JHG}[/tex].
[tex]\fbox{\begin\\\ \begin{aligned}\angle\text{GJH}&=\angle\text{JGF}\\ \angle\text{GHJ}&=\angle\text{GFJ}\\ \text{JG}&=\text{JG}\end{aligned}\\\end{minispace}}[/tex]
So, as per the concept of AAS congruence theorem the two triangles [tex]\triangle\text{FJG}[/tex] and [tex]\triangle\text{JHG}[/tex] are the congruent triangles.
Therefore, the theorem according to which the triangles [tex]\triangle\text{FJG}[/tex] and [tex]\triangle\text{JHG}[/tex] are congruent is [tex]\fbox{\begin\\\ \bf {AAS congruence theorem}\\\end{minispace}}[/tex].
Learn more:
1. A problem to complete the square of quadratic function https://brainly.com/question/12992613
2. A problem to determine the slope intercept form of a line https://brainly.com/question/1473992
3. Inverse function https://brainly.com/question/1632445
Answer details
Grade: Middle school
Subject: Mathematics
Chapter: Congruency
Keywords: Congruency, congruent, congruent triangles, AAS, SSS, SAS, HL, angles, sides, quadrilateral, theorem, postulate, geometry, mathematics, hypotenuse.
Related Questions
At
6:00 A.M. the temperature was 33°F. By noon the temperature had
increased by 10°F and by 3:00 P.M. it had increased another 12°F. If at
10:00 P.M. the temperature had decreased by 15°F, how much does the
temperature need to rise or fall to return to the original temperature
of 33°F?
A)
Fall 7°F
B)
Rise 7°F
C)
Fall 3°F
D)
Rise 3°F
Answers
12:00 p.m. the temperature increased by 10 F so it is 43 F
3:00 p.m. the temperature increased by another 12 F making it 55 F
At 10:00 p.m. it would decrease by 15 F making it 40 F.
The temperature would need to fall/decrease 7 F to reach the original temperature of 33 F so it would be A.
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An architect is designing a new windmill with four sails. In his sketch the sails center of rotation is the origin (0,0) and the top of one sails point T, has a coordinates (6,-2). He wants to make another sketch that shows the windmill after sails have rotated 180* degrees about their center of rotation. What would be the coordinates of T?
Answers
The coordinates of T are (-6,2).
The sails center of rotation is the origin (0,0)
The top of one sails point T(6,2).
What is the rotation?The action or process of rotating on or as if on an axis or center.
A 180 degree rotation make you turn (x, y) into (-x, -y),
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Answers
4x + 66 = 7x + 15
Subtract 4x to both sides.
66 = 3x + 15
Subtract 15 from both sides.
51 = 3x
Divide.
17 = x
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Find the GCF of 44j5k4 and 121j2k6.
Answers
Answer:
The GCF is [tex]11j^{2} k^{4}[/tex]
Step-by-step explanation: I did the assignment on edge.
35+-20+-5 What is the answer?? Worth 10pts...
Answers
If two signs are different they make a negative, if two signs are the same, they make a positive:
[tex]35 - 20 - 5[/tex]
[tex]10[/tex]
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a jigsaw puzzle has edge pieces and inside pieces. the ratio 3:22. there are 924 inside pieces. calculate the total number of pieces in the puzzle
Answers
The jigsaw puzzle has a total of 1050 pieces, with 126 edge pieces and 924 inside pieces, based on the ratio 3:22 provided in the question.
To calculate the total number of pieces in the jigsaw puzzle, we need to use the given ratio of edge pieces to inside pieces, which is 3:22. If there are 924 inside pieces, and the ratio of edge pieces to inside pieces must remain constant, we can set up a proportion where the number of edge pieces is represented by x and the number of inside pieces by 924.
3:22 = x:924
To find the value of x, we can cross-multiply:
3 * 924 = 22 * x
This gives us :
2772 = 22x
Now, we can solve for x by dividing both sides of the equation by 22:
x = 2772 / 22
x = 126
This means there are 126 edge pieces. To find the total number of pieces in the jigsaw puzzle, we add the edge pieces to the inside pieces:
Total pieces = edge pieces + inside pieces = 126 + 924 = 1050
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Answers
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Answers
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Answers
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Answers
Answer:
d.51
Step-by-step explanation:
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Answers
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Using a simple calculation:
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sanjay can travel 342 miles in 6 hours. at this rate, how far can he travel in 5 hours?
Answers
342/6= 57mph
57*5= 285
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SHOW ME THE CORRECT ANSWER DRAW!!
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Answers
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Answers
2x + 2 = 3x - 52
Solving:
54 = x
Hope this helps!
2x - 3x = -2 - 52
- x = - 54
x = 54
hope this helps
Suppose there are 20 questions on a multiple choice test.if 25%of the answers are choice B how many of the answers are not choice B
Answers
f(x)=-x^2+8x-20 find the min/max value
Answers
-b/2(a)
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f(4)=-4
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Answers
Answer:
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First approximation:
192/12 ≈ 14
12*14 = 168 < 192
Second approximation:
192/12 ≈ 20
12*20 = 240
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Third approximation:
192/12 ≈ 16
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Then, 16 is the correct answer
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Answers
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Answers
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56/x^2-2x-15 - 6/x+3 = 7/x-5
Answers
of the 460 visitors on saturday 54/100 of them stayed until the park closed about how many visitors stayed the park closed?
Answers
Hope this was helpful
460*.54=
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248
A scuba diver is 3.8 meters below the surface of the water. He is descending at a rate of 0.5 meters per minute.
Part 1:
Write an algebraic expression to describe the depth of the scuba diver after any number of minutes.
Part 2:
Describe what the variable represents in this situation.
Answers
the variable (m) represents number of minutes
Answer:
[tex]-3.8-0.5x[/tex]
Step-by-step explanation:
A scuba diver is 3.8 meters below the surface of the water.
So, Depth of scuba driver is - 3.8 m
He is descending at a rate of 0.5 meters per minute.
So, Rate = -0.5 m . min
So,Distance traveled in x minutes = -0.05 x
So, The depth after x minutes = -3.8-0.5x
So, an algebraic expression to describe the depth of the scuba diver after any number of minutes is -3.8-0.5x
The variable x represents the no. of minutes .
need help with this if someone could help me please and thank you
Answers
Hope this helps!!
A group consisted of two girls for every boy. 24 more girls joined the group. there are now five girls for every boy. how many boys are in the group?
Answers
If Bella runs 40% as fast as Thomas and 35% as fast as tam what percent faster than Thomas is tam
Answers
Plot the x- and y-intercepts to graph the equation. y=1/3x−1.
Answers
x-intercept= (3,0)
y-intercept= (0,-1)
Answer:
The graph of given equation is shown below.
x-intercept is 3 and y-intercept is -1.
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{1}{3}x-1[/tex]
We need to draw the graph of given equation.
At x=0,
[tex]f(0)=\frac{1}{3}(0)-1=-1[/tex]
So, y-intercept is -1.
Equate f(x)=0 to find x-intercept.
[tex]\frac{1}{3}x-1=0[/tex]
[tex]\frac{1}{3}x=1[/tex]
Multiply both sides by 3.
[tex]x=3[/tex]
So, x-intercept of the line is 3.
Plot these two points (0,-1) and (3,0) on coordinate plane and connect them by a straight line.