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Unit 3 Lesson 8 Cumulative Practice Problems
1. This is an invalid proof that all isosceles triangles are similar. Explain which step is
invalid and why.
1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF.
2. Dilate triangle ABC to a new triangle A'B'C using center C and scale factor de so
that A'C = B'C = DF = EF.
3. Translate by directed line segment CF to take A'B'C to a new triangle A"B" F.
Since translation preserves distance, A" F = A'C= DF and B" F = BC = EF.
4. Since A" F = DF, we can rotate using center F to take A" to D.
5. Since B" F = EF, we can rotate using center F to take B" to E.
6. We have now established a sequence of dilations, translations, and rotations that
takes A to D, B to E, and C to F, so the triangles are similar. ​

Sagot :

Answer:

Step-by-step explanation:

Let ABC be an isosceles triangle with lateral sides AB and AC, a base of BC, and medians of AC and AB, respectively, at BD and CE.

In  △ACE  and  △ABD ,

AB≅AC  lateral sides of isosceles triangle

∠A≅∠A  common angle

AE≅AD  half segments of equal lateral sides

As a result, ACE ≅ABD according to the side angle side theorem. as a result, median BD is consistent with median CE.

If any two figures can be positioned exactly over one another, the congruence between them can be seen. The relationship between two figures is referred to as their congruence, and is expressed using the word "congruence".

In other terms, two geometric figures are said to be congruent if they can be superimposed on one another.

All figures, including triangles, quadrilaterals, and other shapes, have this feature. Along with figures, line segments and angles that have the same measure are also said to be congruent. To comprehend what congruent figures represent, look at the following figure.

To learn more about congruency

brainly.com/question/13995995

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