Answer:
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Step-by-step explanation: cause i know it ❤
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The side of the small triangle that will correspond to the side of HI is side IK.
<h3>How to find corresponding side of similar triangles?</h3>
Similar triangles are triangles that have the same shape but different size.
In similar triangles, corresponding sides are always in the same ratio.
The corresponding angles are equal.
Therefore, the side of the small triangle that will correspond to the side of HI is side IK.
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Refer to attachment for solution ~
If points A, E and C are colinear, then they lie on the same line. The same statement you can say about points B, F and D.
1. Consider triangles AOC and BOD. In these triangles:
- AO≅OB (given);
- CO≅OD (given);
- ∠AOC≅∠BOD (as vertical angles).
Thus, ΔAOC≅ΔBOD by SAS Postulate (If any two corresponding sides and their included angle are the same in both triangles, then the triangles are congruent). Corresponding parts of congruent triangles are congruent, then
- AC≅BD;
- ∠ACO≅∠BDO;
- ∠CAO≅∠DBO.
Since angles ACO and BDO are alternate interior angles between lines AE and BF with transversal CD and these angles are congruent, then lines AE and BF are parallel.
This gives you that
2. Consider triangles ECO and FDO. In these triangles
- ∠CEO≅∠OFD (previous proof);
- CO≅OD (given);
- ∠ECO≅∠ODF (previous proof).
Therefore, ΔECO≅ΔFDO by AAS Postulate (if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent). Then CE≅FD.
3. Note that
Since AC≅BD and CE≅DF, then AE=AC+CE=BD+DF=BF.
