Solve the Proportion: Finding the Missing Term in AD/_ = AE/AC

BC is parallel to DE.

Fill in the gap:

AD=AEAC \frac{AD}{}=\frac{AE}{AC}

AAABBBCCCDDDEEE

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's fill in what's missing.
00:10 Notice, the lines are parallel, just as given.
00:15 For parallel lines, matching, or corresponding angles, are equal. We call this angle A.
00:23 And here, another corresponding angle is equal. Let's call this angle A2.
00:29 So, the triangles are similar because of Angle-Angle, or AA.
00:35 Now, corresponding sides face these equal angles. This helps us understand their relationship.
00:55 And that's how we solve this question!
00:59 Now, let's move on to the next chapter.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

BC is parallel to DE.

Fill in the gap:

AD=AEAC \frac{AD}{}=\frac{AE}{AC}

AAABBBCCCDDDEEE

2

Step-by-step solution

Since we are given that line BC is parallel to DE

Angle E equals angle C and angle D equals angle B - corresponding angles between parallel lines are equal.

Now let's observe that angle D is opposite to side AE and angle B is opposite to side AC, meaning:

AEAC \frac{AE}{AC}

Now let's observe that angle E is opposite to side AD and angle C is opposite to side AB, meaning:

ADAB \frac{AD}{AB}

3

Final Answer

AB

Practice Quiz

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If it is known that both triangles are equilateral, are they therefore similar?

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