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Nadya [2.5K]
3 years ago
14

Read the proof. Given: AB ∥ DE Prove: △ACB ~ △DCE We are given AB ∥ DE. Because the lines are parallel and segment CB crosses bo

th lines, we can consider segment CB a transversal of the parallel lines. Angles CED and CBA are corresponding angles of transversal CB and are therefore congruent, so ∠CED ≅ ∠CBA. We can state ∠C ≅ ∠C using the reflexive property. Therefore, △ACB ~ △DCE by the AA similarity theorem. SSS similarity theorem. AAS similarity theorem. ASA similarity theorem.
Mathematics
2 answers:
Arturiano [62]3 years ago
6 0

Answer: AA similarity theorem.

Step-by-step explanation:

Given : AB ∥ DE

Prove: ΔACB ≈ ΔDCE

We are given AB ∥ DE. Because the lines are parallel and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines. Angles CED and CBA are corresponding angles of transversal CB and are therefore congruent, so ∠CED ≅ ∠CBA.

Also ∠C ≅ ∠C using the reflexive property.

Therefore by AA similarity theorem , ΔACB ≈ ΔDCE

  • AA similarity theorem says that if in two triangles the two pairs of corresponding angles are congruent then the triangles are similar .
noname [10]3 years ago
6 0

Answer:

AA

Step-by-step explanation:

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Lubov Fominskaja [6]
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In ∆FDH, angle D is already given to us as the measure of 80°. We can find out the measure of the other angles of this triangle by using the equation:

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Subtract 80 from both sides of the equation.

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Divide both sides by 2.

x = 50

This means that angle F and angle H in ∆FDH both measure 50°.

Now, moving over to the next smaller triangle in the picture is ∆DHG. In this triangle, there are also two legs that are congruent which once again indicates that this triangle is isosceles.

First, we have to solve for angle DHG and we do that by using the information obtained from solving for the angles of the other triangle.

**In geometry, remember that two or more consecutive angles that form a line will always be supplementary; the angles add up to 180°.**

In this case angle DHF and angle DHG are consecutive angles which form a linear pair. So, we can use the equation:

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Now that we know the measure of one angle in ∆DHG, we can use the same method as the previous step for solving the missing angles. Use the equation:

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The other two missing angles of ∆DHG are 25°. This means that the measure of angle 1 is also 25°.

Solution: 25°
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