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4 years ago

Write a two-column proof. Given: Quadrilateral GKJH is a parallelogram Prove: △GLH ≅ △JLK

Mathematics

1 answer:

klio [65]4 years ago

4 0

Answer:

See explanation

Step-by-step explanation:

Statement Reason

1. GKJH is a parallelogram - Given

2. GH║KJ - Definition of the parallelogram

3. ∠HGL and ∠KJL are alternate interior angles - Definition of alternate interior angles

4. ∠HGL≅∠KJL - Alternate interior angles theorem

5. GH≅KJ - Property of parallelogram

6. ∠GLH and ∠JLK are vertical angles - Definition of vertical angles

7. ∠GLH≅∠JLK - Vertical angles thoerem

8. ΔGLH≅ΔJLK - AAS postulate

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lesantik [10]

Answer:

Students 3 and 4 have green discs. Students 1, 2, and 5 have red discs.

Step-by-step explanation:

If Student 1 is telling the truth, Students 2 and 3 must be lying. If that were true, Student 1 would see at least 2 red discs, not 1. So Student 1 is lying, and therefore has a red disc.

Therefore, Student 5 is also lying, and must also have a red disc.

If Student 2 is telling the truth, the other four students must be lying. That means Student 2 would have a green disc, and the other four would have red discs. But if that were true, then Student 3 would be telling the truth. Therefore, Student 2 is lying.

So far, we know Students 1, 2, and 5 are lying. If Student 3 is telling the truth, then she and Student 4 each have a green disc. If Student 3 is lying, then all five students would have red discs, which would mean Student 2 was telling the truth.

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3 years ago

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svetoff [14.1K]

Answer:

20%

Step-by-step explanation:

1/5 of 1 hour = 20 minutes

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4 years ago

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

How do you use special right triangles to solve for missing sides? (30-60-90 and 45-45-90 triangles)

Assoli18 [71]

Answer: see below

Step-by-step explanation:

30 - 60 - 90 triangles have angles in the triangle measuring 30, 60, and 90 degrees. A 30 - 60 - 90 triangle also has special side ratios according to a side's location in the triangle.

The side across from the 30 degree angle is represented by x.

The side across from the 60 degree angle is represented by x $\sqrt{3}$ .

The side across from the 90 degree angle is represented by 2x.

45 - 45 - 90 triangles have angles in the triangle measuring 45, 45, and 90 degrees. A 45 - 45 - 90 triangle has special side ratios similar to the 30 - 60 - 90 triangle.

The side across from either of the 45 degree angles is represented by x.

The side across from the 90 degree angle is represented by x $\sqrt{2}$ .

These ratios can be used to find missing sides. If you know that a triangle is one of these special triangles and you also know one of its side lengths, you can plug the known length in for x in the proper place.

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