Given the parameters in the diagrams, we have;
4. ∆ABC ≈ ∆DEF by ASA
5. UW ≈ XZ by CPCTC
6. QR ≈ TR by CPCTC
<h3>How can the relationship between the triangles be proven?</h3>
4. The given parameters are;
<B = <E = 90°
AB = DE Definition of congruency
<A = <D Definition of congruency
Therefore;
- ∆ABC ≈ ∆DEF by Angle-Side-Angle, ASA, congruency postulate
5. Given;
XY is perpendicular to WZ
UV is perpendicular to WZ
VW = YZ
<Z = <W
Therefore;
∆UVW ≈ ∆XYZ by Angle-Side-Angle, ASA, congruency postulate
Which gives;
- UW is congruent to XZ, UW ≈ XZ, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
6. Given;
PQ is perpendicular to QT
ST is perpendicular to QT
PQ ≈ ST
From the diagram, we have;
<SRR ≈ <PRQ by vertical angles theorem;
Therefore;
∆QRP ≈ ∆TRS by Side-Angle-Angle, SAA, congruency postulate
Which gives;
- QR ≈ TR by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
Learn more about congruency postulates here:
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Answer:
The given question is
<em>
Draw two 1 dm squares on a sheet of paper. Draw a diagonal on each one and cut them out.</em>
<em />
So, you need to draw square with sides of 1 dm. However, first, you need to transform from dm to cm.
We know that 1 decimenter (dm) equals 10 centimeters (cm).
That means the square sides are 10 centimerers long. So, you need to draw two squares like the first image attached shows.
Then, to draw their diagonals, you need to draw a line segment from one corner to its opposite corner, you should have an inclined line acroos each square. As the second image attached shows.
There you have it. Two squares of 1 dm side with on diagonal each.
Answers:
x = 8
y = 15*sqrt(2)
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Explanation:
This is a 45-45-90 triangle. The right triangle is isosceles.
This means the two legs 3x-9 and x+7 are the same length
3x-9 = x+7
3x-x = 7+9
2x = 16
x = 16/2
x = 8
If x = 8, then each leg is...
3x-9 = 3(8)-9 = 24-9 = 15
x+7 = 8+7 = 15
Each leg is 15 units long to help confirm we have the correct x value.
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The hypotenuse y is exactly sqrt(2) times that of the leg length.
Therefore, y = 15*sqrt(2) since earlier we found each leg is 15 units long.
15*sqrt(2) = 21.213 approximately
Answer:
(1,3)
Step-by-step explanation:
A solution to the equation is any point on the line. You described (-3,-2) and (1,3) being joined on the line. These are the possible solutions without having a graph. Of the options listed, only (1,3) is present. This is the solution.
