Question

ii. set up an equation and then solve for the variable.

1. △cat ≅ △dog. find x.
2. △ief ≅ △hgf. find a.
3. △abd ≅ △cdb. find x.
4. △abd ≅ △cdb. find y.
5. △abc ≅ △adc. find y.
6. △pqr ≅ △mnr find x.

Explanation:

Question 9

Step1: Use congruent triangles property

Since \(\triangle CAT\cong\triangle DOG\), their corresponding sides are equal. So, \(CA = DO\).

Step2: Set up the equation

We have \(8x - 6=3x + 9\).

Step3: Solve for \(x\)

Subtract \(3x\) from both sides: \(8x-3x - 6=3x-3x + 9\), which gives \(5x-6 = 9\).
Add \(6\) to both sides: \(5x-6 + 6=9 + 6\), so \(5x=15\).
Divide both sides by \(5\): \(x=\frac{15}{5}=3\).

Step1: Use congruent triangles property

Since \(\triangle IEF\cong\triangle HGF\), their corresponding angles are equal. So, \(\angle I=\angle H\).

Step2: Set up the equation

We have \(5a=2a + 3\).

Step3: Solve for \(a\)

Subtract \(2a\) from both sides: \(5a-2a=2a-2a + 3\), which gives \(3a=3\).
Divide both sides by \(3\): \(a = 1\).

Step1: Use congruent triangles property

Since \(\triangle ABD\cong\triangle CDB\), their corresponding angles are equal. So, \(\angle ABD=\angle CDB\).

Step2: Set up the equation

We have \(4x-35=2x + 17\).

Step3: Solve for \(x\)

Subtract \(2x\) from both sides: \(4x-2x-35=2x-2x + 17\), which gives \(2x-35 = 17\).
Add \(35\) to both sides: \(2x-35 + 35=17 + 35\), so \(2x=52\).
Divide both sides by \(2\): \(x = 26\).

Answer:

\(x = 3\)

Question 10