Question

1. what additional information do you need to prove △abc ≅ △stu by asa? a. \\(\overline{ac} ≅ \overline{us}\\) b. \\(\overline{bc} ≅ \overline{td}\\) c. \\(\angle a ≅ \angle s\\) d. \\(\angle c ≅ \angle t\\) 31 f is the midpoint of \\(\overline{bd}\\), f is the midpoint of \\(\overline{ac}\\). \\(\triangle abe ≅ \triangle cde\\) by ____ a. aas b. asa c. sas d. sss 32 \\(\overline{ab} \perp \overline{bd}\\) \\(\overline{cd} \perp \overline{bd}\\) \\(\overline{ab} ≅ \overline{cd}\\) \\(\triangle abd ≅ \triangle cdb\\) by __ a. aas b. asa c. sas d. sss 33 \\(\triangle abc ≅ \triangle adc\\) by what reason? a. aas b. asa c. sas d. sss 34 \\(\overline{gl}\\) bisects \\(\overline{hk}\\), \\(\overline{gh} \perp \overline{hk}\\) and \\(\overline{lk} \perp \overline{kl}\\) \\(\triangle ghj ≅ \triangle lkj\\) by __ a. aas b. asa c. sas d. sss 35 find the largest angle in \\(\triangle abc\\) a. \\(\angle a\\) b. \\(\angle b\\) c. \\(\angle c\\) d. not enough information 36 in \\(\triangle pma\\), ____ a. \\(m\angle p > m\angle a\\) b. \\(m\angle p = m\angle m\\) c. \\(m\angle a > m\angle p\\) d. \\(m\angle m = m\angle a\\)

Explanation:

Question 35:

Step1: Recall Triangle Angle-Side Relationship

In a triangle, the largest angle is opposite the longest side. This is based on the theorem that in a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

Step2: Identify the Longest Side in $\triangle ABC$

Given the sides of $\triangle ABC$: $AC = 5$, $AB = 6$, and $BC = 7$. Comparing the lengths, $7$ (length of $BC$) is the longest side.

Step3: Determine the Angle Opposite the Longest Side

The angle opposite side $BC$ is $\angle A$ (since side $BC$ is between vertices $B$ and $C$, so the angle opposite is at vertex $A$). Wait, no, let's correct that. Wait, side $BC$: the vertices are $B$ and $C$, so the angle opposite $BC$ is $\angle A$? Wait, no, in $\triangle ABC$, side $BC$ is opposite angle $A$, side $AC$ is opposite angle $B$, and side $AB$ is opposite angle $C$. Wait, let's label the triangle: vertices $A$, $B$, $C$. Side $BC$ is between $B$ and $C$, so the angle opposite $BC$ is $\angle A$. Side $AC$ is between $A$ and $C$, opposite angle $B$. Side $AB$ is between $A$ and $B$, opposite angle $C$. Now, the lengths: $BC = 7$ (longest), so angle opposite $BC$ is $\angle A$? Wait, no, wait the side lengths: $AC = 5$, $AB = 6$, $BC = 7$. So side $BC$ is the longest, so angle opposite $BC$ is $\angle A$? Wait, no, maybe I mixed up. Wait, let's list the sides and their opposite angles:

• Side $BC$: opposite $\angle A$
• Side $AC$: opposite $\angle B$
• Side $AB$: opposite $\angle C$

So the longest side is $BC = 7$, so the largest angle is $\angle A$? Wait, no, wait the side lengths: $AC = 5$, $AB = 6$, $BC = 7$. So $BC$ is the longest, so angle opposite $BC$ is $\angle A$. Wait, but let's check again. Wait, in triangle $ABC$, with sides $AC = 5$, $AB = 6$, $BC = 7$. So the sides in order: $5 < 6 < 7$. So the angles opposite these sides will be in the same order. So the smallest angle is opposite the smallest side, and the largest angle is opposite the largest side. So side $BC = 7$ (largest side) is opposite angle $A$, so angle $A$ is the largest? Wait, no, wait the labels: the triangle is labeled with $C$ and $B$ at the base, $A$ at the top. So side $BC$ is the base, length 7. Then $AC = 5$ (from $A$ to $C$), $AB = 6$ (from $A$ to $B$).[LLM SSE On Failure]

Answer:

Step1: Recall Triangle Angle-Side Relationship

In a triangle, the largest angle is opposite the longest side. This is based on the theorem that in a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

Step2: Identify the Longest Side in $\triangle ABC$

Given the sides of $\triangle ABC$: $AC = 5$, $AB = 6$, and $BC = 7$. Comparing the lengths, $7$ (length of $BC$) is the longest side.

Step3: Determine the Angle Opposite the Longest Side

The angle opposite side $BC$ is $\angle A$ (since side $BC$ is between vertices $B$ and $C$, so the angle opposite is at vertex $A$). Wait, no, let's correct that. Wait, side $BC$: the vertices are $B$ and $C$, so the angle opposite $BC$ is $\angle A$? Wait, no, in $\triangle ABC$, side $BC$ is opposite angle $A$, side $AC$ is opposite angle $B$, and side $AB$ is opposite angle $C$. Wait, let's label the triangle: vertices $A$, $B$, $C$. Side $BC$ is between $B$ and $C$, so the angle opposite $BC$ is $\angle A$. Side $AC$ is between $A$ and $C$, opposite angle $B$. Side $AB$ is between $A$ and $B$, opposite angle $C$. Now, the lengths: $BC = 7$ (longest), so angle opposite $BC$ is $\angle A$? Wait, no, wait the side lengths: $AC = 5$, $AB = 6$, $BC = 7$. So side $BC$ is the longest, so angle opposite $BC$ is $\angle A$? Wait, no, maybe I mixed up. Wait, let's list the sides and their opposite angles:

• Side $BC$: opposite $\angle A$
• Side $AC$: opposite $\angle B$
• Side $AB$: opposite $\angle C$

So the longest side is $BC = 7$, so the largest angle is $\angle A$? Wait, no, wait the side lengths: $AC = 5$, $AB = 6$, $BC = 7$. So $BC$ is the longest, so angle opposite $BC$ is $\angle A$. Wait, but let's check again. Wait, in triangle $ABC$, with sides $AC = 5$, $AB = 6$, $BC = 7$. So the sides in order: $5 < 6 < 7$. So the angles opposite these sides will be in the same order. So the smallest angle is opposite the smallest side, and the largest angle is opposite the largest side. So side $BC = 7$ (largest side) is opposite angle $A$, so angle $A$ is the largest? Wait, no, wait the labels: the triangle is labeled with $C$ and $B$ at the base, $A$ at the top. So side $BC$ is the base, length 7. Then $AC = 5$ (from $A$ to $C$), $AB = 6$ (from $A$ to $B$).[LLM SSE On Failure]