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:
935
Step-by-step explanation:
Let's solve the rectangle first. We are dividing this figure into two sepreate shapes, can you see that?
-
1/2*B*h
630
-
Now for the other shape.
Volume = 315
630+315=935
It should be noted that a pantograph consists of four rods that are joined together in order to form a parallelogram with the joints varying in relation to the scale of reproduction.
<h3>
Pantograph</h3>
In a pantograph, the mechanical assembly is based on the shape of a parallelogram.
It should be noted that the operation of a pantograph can be related to dilation as it has a fixed center and two points which are a drypoint that follows the contour of the original drawing, as well as a pen point that traces the reproduction in an enlarged or reduced form.
In order to enlarge a drawing, the index is positioned between the fixed center and the pen. Therefore, to reduce it, the pen is set between the fixed center and the index.
Lastly, to copy a drawing on the same scale, it can be deduced that the index and the pen are equidistant from the fixed center.
Learn more about mechanical assembly on:
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