for each pair of triangles, determine whether the hypotenuse-leg (hl) congruence property can be used to prove that the triangles are congruent. if necessary, you may learn what the markings on a figure indicate. (a) can the hl congruence property be used? yes no (b) can the hl congruence property be used? yes no (c) can the hl congruence property be used? yes no (d) can the hl congruence property be used? yes no

Question

Accepted Answer

### Part (a)
# Explanation:
## Step1: Recall HL Congruence
HL (Hypotenuse - Leg) Congruence applies to right - angled triangles. It states that if the hypotenuse and one leg of a right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, then the two triangles are congruent.
In figure (a), we have two right - angled triangles (marked with right - angle symbols). The legs of the right - angled triangles are marked as equal (the tick marks) and they share the hypotenuse (the diagonal side). So, we can apply the HL Congruence property.
## Step2: Determine the answer
Since the two triangles are right - angled, have a common hypotenuse, and one pair of legs are equal, the HL Congruence property can be used.
# Answer: Yes

### Part (b)
# Explanation:
## Step1: Recall HL Congruence
HL Congruence is for right - angled triangles. We need to check if we have a hypotenuse and a leg equal.
In figure (b), we have two right - angled triangles. The marked sides are the legs (not the hypotenuse) and we don't know about the hypotenuse. HL requires hypotenuse and one leg, but here we only have information about the legs (the marked sides) and not the hypotenuse. So, we can't apply HL Congruence.
## Step2: Determine the answer
Since we don't have the hypotenuse - leg combination required for HL (we only have leg - leg information for the marked sides and no information about the hypotenuse), the HL Congruence property cannot be used.
# Answer: No

### Part (c)
# Explanation:
## Step1: Recall HL Congruence
HL Congruence is applicable only to right - angled triangles. In figure (c), the triangles are not right - angled (no right - angle marks). So, HL Congruence (which is for right - angled triangles) cannot be applied.
## Step2: Determine the answer
Since the triangles are not right - angled, HL Congruence (which is a congruence criterion for right - angled triangles) cannot be used.
# Answer: No

### Part (d)
# Explanation:
## Step1: Recall HL Congruence
HL Congruence is for right - angled triangles. The formula for the hypotenuse $c$ of a right - angled triangle with legs $a$ and $b$ is $c=\sqrt{a^{2}+b^{2}}$. For a right - angled triangle with leg $a = 8\space cm$ and hypotenuse $c = 17\space cm$, we can find the other leg $b$ using $b=\sqrt{c^{2}-a^{2}}=\sqrt{17^{2}-8^{2}}=\sqrt{289 - 64}=\sqrt{225}=15\space cm$.
In figure (d), we have two right - angled triangles (marked with right - angle symbols). One leg is $8\space cm$ (for both) and the hypotenuse is $17\space cm$ (for both). So, the hypotenuse ($17\space cm$) and one leg ($8\space cm$) of one right - angled triangle are equal to the hypotenuse ($17\space cm$) and one leg ($8\space cm$) of the other right - angled triangle. Thus, HL Congruence can be applied.
## Step2: Determine the answer
Since the two right - angled triangles have hypotenuse $17\space cm$ and leg $8\space cm$ equal, the HL Congruence property can be used.
# Answer: Yes

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QUESTION IMAGE

Question

Explanation:

Part (a)

Step1: Recall HL Congruence

Step2: Determine the answer

Step1: Recall HL Congruence

Step2: Determine the answer

Step1: Recall HL Congruence

Step2: Determine the answer

Answer:

Part (b)